Quote "2) A fuel-related miss. I can’t discern a transitional stumble between the various carb circuits. The accelerator pump gives a good shot. The miss is present both during the acceleration and as you hold it at an elevated RPM. (Possible clue: I do have a leak at the throttle shaft. You won’t see it while running, but definitely will if you open the throttle not running)" End quote
Billions of pixels have been unnecessarily disturbed on the internet on this subject.
AS A GENERAL RULE ON SINGLE BARREL CARBURETORS:
Original clearance from throttle shaft to throttle body would have been 0.004~0.006 inches. WEAR HAPPENS! Again, the general rule being that an additional 0.003 is acceptable. Measure the clearance WITH A DIAL INDICATOR, NOT CLICK CLICK BETWEEN YOUR THUMB AND FOREFINGER!

If the clearance is less than 0.010, forget it.
If the clearance is 0.010 or greater, then what???
Excessive clearance MAY influence idle quality (set the idle 50 RPM higher, unless you have a dogmatic transmission, in which case change it for a real transmission

). It may also cause a hesitation (again, with a dogmatic transmission) when transitioning from idle to off-idle.
Excessive clearance will have very little to no effect once the engine is running on the main circuit of the carburetor.
When I was still restoring carburetors, have had several tractor carburetors with 5/16 inch throttle shafts come in where at least half of the shaft was worn away. That is correct, more than 0.100 clearance. The tractor would not idle, but ran at P.T.O. speed just fine. Tractors have governors, and one with a fatigued governor spring will just beat the throttle shaft to death.
Personally, I think Martin is correct; but I believe in testing. How about a compression test, followed by a leakdown test, to check internal engine condition?
Jon