Backfiring issue

If I read your description right, you've had the car for awhile and the engine had been running well?

It sounds like it wasn't kept up though, ie: the dirty cap, rotor and dirty carb? Does it run on points? they might be bad too.
Like somebody mentioned above, don't overthink this but now that you've messed with the timing and carb adjustments you're gonna have to go back to the beginning.

First I'd find TDC, then set the timing to around 12 degrees. If it won't start then adjust the timing in tiny tiny amounts until it starts.
Also it sounds like you have your carb throttle (curb idle) open too far, back that off and set the mixture screws to 1 1/2 turns out evenly. If it won't idle do not be tempted to open the throttle more, you need to adjust the timing again so it idles where you want off the timing. If you have the throttle open too far it's sucking gas in and you will experience the off idle "hesitation" you've already described.

Good luck!