Sounds like you have covered all the bases with the carb. After that, I'm out, as I have no experience or knowledge on the 360/400 bikes. Other than routine stuff which would apply to all the bikes.
Good luck!

if you got compression, fuel and spark then you would aleady zipping past jealous neighbors 

if you can keep it running as long as your squiring ether into her (unlubricated ) then this hack thinks your spark/timing is close enough, leading me to think you have a fuel issue. 

I recently rebuilt card on my DT1E and missed lining up the "jet, needle jet" axial slot with the locating pin and had a siphoning issue until I fixed this.  I had gas in the bowl but she wouldn't run unless chocked...just an idea

whatever you do change the brake shoes before going on a ride above 10 mph

Have you had the mag cover off and had a look in there.  Lots of times the mag area is full of effervesence and rirt and aluminum and it will damage the pulser permanently.  This is your symptom  misfiring  backfiring and quitting totally when hot  unexpectdly.
Doug

Check the pulser in the mag  It must be 90 to 100 ohms or the ignition will be intermittent  the green/white and red/white wires.  if you get below 90 ohms here you will have a poor ignition on no ignition
Doug

How do I check the pulser?
my flywheel is super rusty too. How should I be cleaning it?
does this look super bad?

Looks like yu have two post going on this. If it runs on start fluid it does still sound like the carb is blocked. If its got that side main jet in the bowl then it all starts from there. Does it suck if you put your hand over the carb with throttle open. Choke jet in the cavity in the bowl is prone to blockage, then if you open the choke it give more air making a bad situation eve worse if no fuel added from the fixed jet down the cavity.

As previously stated, the carb is basically brand new. Yes the engine creates vacuum