Ah, now I read ya, It gets worse/starts to happen.

 

I should do more testing to be sure.

 

Okay, I'm back from a look -- the car is definitely dying, now even when cold when:

I put it into gear and don't feather the accelerator up to 1500 (fuel supply is VERY suspect, I should add -- this tank has not yet been cleaned and I plan to swap out the filter to have a go).

It is idling at just a shade under 1000 rpm.

The air injection system , I believe, has been removed and the line plugged (I will endevour to get a photo of that) to show. The air pump has been removed. This does point to me that I should have a hard look at the vacuum system, I think.

My plan of attack: Replace fuel filter and see if the issue gets resolved there.
Learn about how the vacuum line should look and how to diagnose issues with it (any pointers on that would be appreciated).

Sound solid? Suggestions are welcome for the home mechanic

 

many people remove the air pump system plugging the cylinder head line connections with bolts so that's not an issue.

Idling is fine between 800 and 900 rpm. 1,000 is a bit high.

 

Okay, good to know.

 

Did you figure this out? I have the same issue

 

Yes: fuel starvation caused by blocked fuel tank feed lines. Had to replace entire fuel line set from stem to stern. That XK engine is a great little burro, but it's being asked to pull a very heavy wagon, and won't accept anything less than a full stream of high-octane carrots for its meal.

Benefit to me: I learned how to pressure test a fuel injection circuit.