If you have that much difference in the heat coming from your pipes then it is definitely a fuel mixture problem.
The one's not getting hot are running "lean" and this also explains your backfire on #4.
When you try to rev a motor and don't supply enough gas it will cough (backfire) as it attempts to do what you are asking of it.
The supply of gas to the lean cylinders is not sufficient to allow for constant even running so they don't heat like the one's getting good gas supply, hope I have explained that OK.
A really good guage of what your motor is doing is by removing all 4 plugs, yeah I know it's a PITA but gives you a real feel for what's happening inside your combustion chambers.
A good sync job should cure most of your problems unless there is a physical blockage somewhere.
Buying carbs off Ebay is like Russian roulette, you still wont know who stuffed with them or how long they have been sitting around off the bike......in saying that I have a rack of duplicate 79 carbs I use for parts and learning when my bike plays up, your call but $110 would buy a damn good carb sync from an expert.