Will it idle ok, and backfires only when you try to accelerate? If so, check to see that the accelerator pump is adjusted correctly and with key off work the accelerator while looking down in the carb to confirm a good shot of fuel going in. No accelerator pump shot = violent backfire through the carb. The choke has to be working and correctly adjusted or it will cause this problem until the motor is pretty much warmed up, also.. I'm looking at a pic of the carb and I see a vacuum - operated choke pull-off. That has to be right, too. The backfires could have possibly blown the little rubber diaphram in it and caused it to not work and become a vacuum leak at the same time. All that stuff has to work together correctly to make the total package.
The compression test will tell you if an intake valve is burnt, but I honestly doubt that its the problem as this seemed to crop up after the carb rebuild.. I would definitely check the timing with a good advance light, the dist could have got loose and moved.. Lots of stuff to look at
