So without actually seeing you adjust valves --- I think that is part of the problem -- I'd START with a fresh valve adjustment using the techniques in the video.
This is CRITICAL regardless of hydraulic of solid.... and done wrong -- you'll have valves not seating fully - or valves open when they shouldn't be etc.
The backfires and gas burning in the muffler kinda leads me to think there's a bit of an issue there... Carbs don't backfire... so that is either timing --- or valve adjustment.
You're not going to know about the valves unless you just do it over with the info you've been given. Personally I use a felt tip pen and mark "I" or "E" on the head gasket surface so when I'm rolling 'em around -- I know which valve I'm working on.
Then when I was done with that --- I'd leave it so that I can watch the valve on number 1 both closed --- watching the ROTOR on the distributor -- and roll it till the timing mark is at TDC.... ALL THOSE THINGS SHOULD MATCH UP -- ROTOR on #1 -- valves on #1 closed after the INTAKE opens and comes closed -- and the timing balancer and pointer on TDC.
At that point -- I'd make a felt pen mark on the dist where the rotor is EXACTLY -- and another where the rotor ends up after she clears the cam gear (gives you a good starting point for the re-stab) -- I'd pull the distributor --- work the advance making sure she's free and snappy -- and check that the stop bushing is where it should be and there's no interference with it.... Stab it back in... after checking that the rotor is where it should be (there should be a square peg on one side)... that it seats properly -- and that the CAP looks good etc.
I'd fire it at this point and see if anything has improved -- set your timing ....
THEN I'd mess with the carb.... but not until I KNEW FOR SURE the valves and the timing are good. Carbs are DUMB -- they don't control much except the idle.