Thanks for the responses guys. 

This is why i've been slow to take the car to an expert.  This is THE british car shop in town, and all I got was $165 bill for adjusting my valves, which I had just done.  (he did say they were very close just a tiny bit loose). Then they wanted to do a $2400 timing chain job, but was still skeptical if that would fix the issue.

It DOES still feel like a fuel delivery issue.  I replaced my SU original pump with a facet pump 41-2010-8 a while back.  No change.  Do you guys really think getting a new SU pump could fix the problem?  If yes, then I'll do it.  

I'll look into checking the lobes. 

I have replaced all fuel lines.  & cleaned the fuel tank.  It is clean. I have a clear fuel filter right in front of the carb.  It is never empty.

Quick recap on the problem. UPDATED.

while sitting still in the driveway, if I hold the throttle open at 4000rpm the engine runs smoothly for 1 to 1 1/2 minutes.  then begins to clack and sputter. until I let it idle for a few seconds.  then will run smoothly again. I can repeat this over and over. But I don't.

"Specialist" don't post what you don't know anything about. If MLM's Mini is the one in his avatar (i can't be bothered to re read this whole thread) and has the original engine it does not have a tensioner but if you had read the Haynes manual you would know that.

MLM don't waste your money on replacing the timing chain unless it is making a noise, i would guess 99% that that is not the problem.I have seen them wear a hole in the cover and still run well.
Have you checked the camshaft to make sure you are getting enough lift and the lobes are not worn down ?

I had a very similar problem I replaced the pump with a new one , all the rubber lines , the fuel filter , plugs , leads, dizzy ,vented the cap (it is on a ute pickup)cleaned the carbs (2x1.5 su) checked the floats  , no improvement . So I went to my local SU supplier while getting some new parts (needles and seats , springs etc) told him about the problem and my attempts at a cure , he instantly through up his hands and said the problem is the pump , I had replaced it like for like with a Quint and Hazel AUF214 which he told me pump not enough volume at too much pressure , so I bought a brand new proper SU AUF214EN installed it took it for a long run and it seems to have worked so my advise for what it is worth is go and buy the proper pump spend the money , they are not cheap , and start from there !!

$2400 to tighten the chain?????????????? Omg !!!  Actually it was the tensioner that has worn out, buy the tensioner, its a hard plastic tensioner  btw, and im sure you can replace it yourself. , remove the   Radiator fan, and the timing chain cover and youll see the tensioner , replace the o seals while you're at it...good luck!

I finally took my mini into the local british car shop.  After looking it over for a week they suspect possibly a very worn timing chain.  I'll probably take this task on myself since they quoted me $2400 and didn't seem extremely confident that it will fix the problem.  I'm going to do it with the engine in the car.  Any advice?  Anything I should get besides the chain & cover gasket?

I didnt read over this very good but seen fuel pump talk and figured id share my past issues with pumps.(not minis though) and sorry,only carb i ever had was on the mini and i didnt have it long ..

I had -10an lines on a car before with a large external fuel pump(electric) It started and ran fine..light driving good...highway speeds it would start choking and cutting out and shut off.There was a filter before and after the pump.Both appeared to be new looking.Called the fuel pump company and they said the filter gets clogged and gels up and is not visual to the eye.Swapped the filter and it was perfect.

Another time i installed the tank after putting a bigger fuel system in and the vent tube got pinched and the car would run for 15 mins then die...opned the fuel filler cap and youd hear the tank release all the pressure.

Also i had an internal tank pump do the same before...pump was fine jist was way too small for my application and any sort of load on the truck or more then 1/2 throttle it would die out .

Also check the lines and make sure it flows through good,sometimes filtets come,apart and clog lines.Never had it happen personally on the fuel side but i did have a nitrous filter clog a nitrous line and couldnt figure out why ut woukdnt work right for a while.

ok, here's my very last question, and i think this is the deciding question:  When did you last replaced the Float valve viton tipped needle and seat?  these parts wear out, it is the most neglected part of the carb.   The fuel pressure goes up at high revs, it might, I'm not saying it does, but the pressure might be defeating the valve stop thus partially richening or flooding the comb chamber and engine starts to bog at 3500 to 4000 rpm, either replace it or use a fuel pressure regulator or do both.....just something to look at...

If by a small miracle the 5 gallon gas tank and new fuel pump work and cure the problem then install the new fuel pump in the car and see if it still works if not then look at the tank and lines.

You maybe using a wrong needle, the way you describe it, it seems like it richens too much when you're at high revs. Buy or Borrow a Gunson tuning kit and address that richness issue. i 've never had my mini pass 3k rpm, i do 2800 to 3k at cruising speed of 45-52shhh. The previous owner of my mini told me that my engines final drive is 5.3 : 1
that's why 1 gallon last me about 48 miles.

it will rev well over 3800.  just a problem cruising. 

this seems similar to how my car acts.  albeit at lower rpms. 

www.youtube.com/watch?v=bW5Q8wub2hA

after hitting the highway (about a 1 mile from my driveway), i can go about 1/4 mile at 3800rpm then it starts stumbling- it actually feels like it's on a rev limiter because it will run like this for a while-  although I have only run it like this for about 15 seconds. Then I can drop speed and it will sort itself out.  Then up the speed a bit to 3800-4000rpm and it stumbles again.  I could do this over and over and over. 
It will rev over 4000rpm. i can get going over 75mph for a short while, everything sounds great- then soon the stumble starts. 

I haven't been able to test the new pump yet because Austin traffic is so bad most of the day you can't get over 40mph even on the highway. 
I will try the 5 gallon tank asap. 

Will it rev past 3800 if you accelerate or is just at cruise you have the problem?

Before you go to the trouble of pulling the tank set up the 5 gallon gas can (or whatever size one) with the new pump you're getting, a lot less hassle and may give you the answer.
I thought in previous posts you said it always stumbled at the same point on the road after leaving your driveway ?
So if you slow down from 3800rpm to 3400rpm when the issue occurs can you continue driving or do you have to pull over and wait a while?
If you are ok at 3400 rpm but not at 3800 rpm fuel delivery would be my guess.

I have not yet tried the alternate gas tank. 
forgot to reroute fuel line.  I'll do that. 
But the problem happens after 2 minutes of driving or 30 minutes of driving.  always cruising at about 3800rpm. I can cruise at 3400rpm all day long. if i pulled to the side of the road it would run fine.  
I have yet to test it with the new fuel pump. I'll test today or tomorrow. 
& pull the tank next week if need be.  

Would seem to be fuel or mechanical issues. Let us know if disconnecting the tach changes anything. Did you re route the fuel line from over the top of the inlet manifold ?
Dan i think i suggested way back to run it with a different fuel source. A 5 gallon gas can and ten feet of fuel hose with a electric pump would eliminate all of his current fuel set up.
Another thought maybe an exhaust valve (due to a tolerance issue in the guide) is sticking open when the car heats up.
If the car does in fact still misfire when stopped check which cylinder has the misfire by pulling the plug wires one at a time and then do a compression check on the side of the road on the cylinder that is missing, let it cool down and re check it. Doing this would at least isolate the problem to 1 or 2 cylinders.

tach does not jump around.
yes. you did suggest valve float.  thanks Dan.
I'll pull the tank soon. hopefully time next week.  

I'll test it with tach disconnected next week.

...as I suggested in my recap (provided for those who don't read the entire thread).
Valve float was suggested as a REMOTE possibility.

MLM: you have checked all the fuel system except the tank screen. That makes it now the prime suspect. Fuel tanks rust. They collect dirt. Sometimes they get a sealer treatment like POR15, which can block the screen (people doing such treatments sometimes don't know about or forget the screen, with fuel delivery problems resulting. Remove the tank and clean it. Remove the screen. If you feel you really need protection before the pump, add a metal filter.

Please excuse me if these questions have been asked before. Does your tachometer jump around or malfunction when this problem occurs ? Is it a factory tach ? Have you driven it with the tach disconnected ?

I'm not judging believe me, but after a year of chasing the same problem it must be a bit gutting at least? As for good mechanics they are out there you just need to find one you can deal with! It's easy for me as I've been a mechanic for over 45 years now dealing with mini's since day one, If I can't suss something out I have a whole host of experts up here at the track to lend a hand. If you have a chassis dynometer/rolling road near you it will probably be the best money you could spend right now to find your problem and get the Carb. and Distributor spot on...................

I dont want to judge anyone, a $48 fuel pump is a goid quality pump, but pls, get an equaly good fuel filter,,a $1.50 fuel filter may be made in Chong Hua.  And more often than not it is clogged   even before you use it.  There is a $9 glass fuel filter that is reusable. Available at your local auto stores.

Remember this, the fuel pump is only good as the fuel filter.