I'm wondering, based on what you said, if the points plate is turned excessively one direction or the other with respect to the general setting and in an effort to properly achieve the timing as you've set it. If it's significantly advanced or retarded from the basic location, it could indicate that you are, in fact, a tooth off on the cam timing - at which point that could be the culprit

 

^^^ What he said. Also the fact that you stated that you have to push the throttle forward to close completely tells me your throttle cable is binding and/or not properly adjusted.
Have you checked for a vacuum leak around the carbs? That too can cause high idle

 

360's back fire quite a bit when their carbs are poorly synced. They are also hard to start and will run sorta kinda. Most times one side will do the work and will tend to want to run faster than the other and drag the other one along. They will NOT want to settle into an idle and they will NOT run smoothly. You should be able to tell which side is doing the work as that side will be hotter than the other and the side the is not doing much work will probably be the one that back fires. You had PJ do the carbs which is awesome but they are not tuned specifically for your bike in your running conditions. I'd Highly suggest hooking up the gauges to your carbs and checking the sync.

PAMCOs are a hit and miss seems like, there's threads all over the interwebs about how they either work or they don't so it sounds like you have one that works for now. The slight lagging of the left side sounds to be common with them. dynamically you want to tune and time a bike for 3-4k RPM running as that is where you are going to be most of the time at least.

 

UPDATES! Hooray!

So I popped the top and redid the cam chain - barring me being just too dumb for this work, it's correctly timed on the cam chain that said, what I DID find was a suspicious little nut laying in one of the oil wells (nearly gave me a heart attack)... one of the lock nuts on the valve clearance adjusters had popped off (the left cylinder intake valve), and I think that was what had it going haywire. Got it sealed back up and tensioned/timed/clearanced, and the idle seems much happier (with very tight lock nuts).

Of course, that's never the end of it, is it? I'm...pretty happy with where the timing is, but it seems like I'm using some of the PAMCO's advance at idle (which I still can't get below 1200). I know the instructions say to get it down to 900-1000 if you can. What's happening is that it's firing almost exactly at the F/LF at the 12-1300 idle, but then I'm probably an 1/8-1/4 inch short of the first mark on the advance range. I just replaced the carb boots with Common Motor ones and new gaskets, so I'm pretty sure there's no vacuum leak there. That said, I'm also only getting like 7 inch/pounds(?) of vacuum on each carb, though they're sync'd correctly - I don't know if that's a symptom of the pods (PO dumped the stock boxes, though PJ rebuilt the carbs for pods), or if I should be looking at the diaphram.

More fun! Took it out for a test ride, and for about 10 minutes it ran pretty well. After that, it'd die the second you start to release the clutch, and it wouldn't be happy to get started again (I suspect battery, though I replaced the thing a year ago). On top of that, after the first 10 minutes, I'd be able to rev it up to 5-6000 and then the revs would start plummeting again, back to idle if it didn't die outright.

TL;DR:
-Can't get the idle below 1200
-Not advancing fully at 3000 RPM
-Maybe low vacuum on both carbs (7 inch/pounds)
-Revs die after 5000 and it dies under any clutch pressure

I know I need to address the idle issue, but I'm not sure where to start. I'm gonna start with a compression test - I split the case and rebuilt it from the ground up last year, with copper head and base gaskets, but I wanna eliminate that. Any other ideas? As always, thank you guys so much for putting up with me

 

Bump. I pulled both plugs yesterday, and it looks like the right is gas fouled (all black and sooty), while the left looks OK but a little wet (I'd been cranking the engine). Any thoughts?

 

Did you get new ignition fitted yet?