Bought the bike for nothing non running. Replaced zener diode and it fired right up for ~30 seconds. Fuel pump was on backwards. Fixed and bike ran.

Had the carbs professionally synced and cleaned, have replaced coolant, oil and now fuel cut off relay.
Was reading 7-8v on one of the wires while the bike was acting up. Now reading 12 on all until the bike dies

The symptoms:
After a warm up period of ~10 minutes, the bike will start to run strange, pretty constant sputtering from the exhaust. Inconsistent power (I have kinda power one moment then almost none, all sputtery the next).
At idle it will idle rough for a few seconds and die.
It will not die when blipping the throttle every second or so.
A new whooshing sound now happens whether cold or hot between 5500-6000 rpm then stops.
Gas tank overflow line is clear. I don't know where the breather is, but popping the fuel cap doesn't really alleviate anything.

 

Took the air filter out. Cleaned the crap out of the 2 bottom Chambers. Ran it with the top of the air box off and it's been backfiring and dying.
Battery is still showing 14ish V at idle
Plugs just changed last night, which seemed to delay the issue a bit. 1 coil is new, and tried with 2 more coils in the center 2 cylinders with no change.

Idle is migrating between 1000-2000 rpm

Pulled headlight fuse to see if it was an electrical issue without change.
Temperature gauge is a little below halfway up, and I have yet to see the fan kick on the entire time I've had the bike

 

When you say you paid to have the carbs sync'd, did they bench sync them or do it in a running bike?

 

He's closed on weekends. I've already called and left a voicemail for him to call me back