If the ignition timing and distributor are in proper condition, then a good chance it has an issue with the accelerator pump in the carb, or sloppy linkage for it that causes a delay in the squirt. There are also two holes in the throttle lever for the accel pump link. The outer hole gives a longer and quicker stroke, if it's not in that hole already.
Also, if it's been backfiring through the carb, it may have ruptured the power valve in the carb. If it has a rich idle now, that may be the issue.
Sal