In addition to what Muthy said..
Spend a bit and put a proper choke cable on and recheck the plunger operation.
That isn't a choke but a fuel enrichment circuit..
Problems there will just mess with your head as you're trying to set up you jets and needle settings.
The backfiring on accel to me says you're running lean on the mid-circuit, but sound like you're rich on your idle circuit since you can start from cold with zero choke.
Start from ground zero and do it again!!
Lastly a compression test wouldn't be a bad idea..an engine with low compression will be impossible to get your carb set right since your intake pressure will be too high.
Current toys..
1986 Honda 350X..trail bomb!
1985 Honda 250SX..my main mudder
1985 Honda 250ES..Back in Black Trike
Current non-trike toys:
1990 Honda TRX300FW
1995 Seadoo GTX
1998 Polaris Indy Lite 340(Nearly new looking)
1998 Polaris Touring 500
1998 Club Car (electric)