Lin/All--
I can't imagine why Welch would suggest driving off immediately since the most important reason to "warm up" an engine--especially a race engine--is to get the oil temperature up a bit so that it offers proper lubricity to critical parts such as bearings, etc. The hesitation, coughing, sputtering, etc that some experience is an inconvenience at most and certainly a secondary issue to one who is racing and will be pushing his engine to the max in, at most, one lap of getting off the grid. As we know, running with the engine "choked" enrichens the mixture which tends to wash lube oil off the cylinder walls--not a good thing.
BTW I am fortunate in that my car is an easy starter and the return springs positively pull the jets back to normal. I am really not familiar with the "choke" setup of later Big Healeys and perhaps my earlier post was not helpful to the original poster, but it would seem to me that the first step in dealing with the issue is to determine whether the bind is in the carb linkage(s) or the choke cable or both.