My old AE82 4AC did the same thing, sometimes it didn't want to go and would bog down, other times it was fine. Because I knew SFA about carbies at the time I never got to iron it out (had it for 5 months).
My guess now would be that you need to tune it, fuel was a very likely cause. If you have a Haynes/Gregory's manual for the car now would be a good time to study the carby section.
I don't know much about the 4AC carby but like most carbies it will need to be checked/tuned/rebuilt every once in a while. Check the float level is a good start.
Again, by what you describe when you're out on the track, weight shifting needs some pumping of the accel which jets extra fuel in. If you were to pump the accel say 3 times and release it immediately each time, you'd be a little overfuelled and so that 10-15 seconds would be the time for that fuel to be used up again.
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