There is a shorty two brothers exhaust and a k&n filter on it. No jet kit. Is that where the problem lies?
I would say thats the very good place to start. Not only can an aftermarket slip-on require a rejet, but you have a k&N filter, plus the aftermarket slip is a shorty. Sometimes, if you only have a slip on, you can get away without having too many issues. but the fact its cut short, will create problems.
About the only thing you can do is jet for your situation, which just installing a stage one or stage two jetkit will probably not solve your issue. Your issue is kind of unique to your bike. You more than likely have a lean condition down low, and maybe an ideal condition up top. You may also still be lean up top though.
Have you pulled your sparkplugs to look at them?
If you don't have any mechanical knowledge with carbs, I would leave it to a professional. Or, go to a full length slip on. that way, you can get a dynojet kit that will fit your bike better, then only a small amount of tweaking will be required instead of the headache your going to have with that set-up.
I know you probably see a lot of shorty exhaust out there, but most of those will be on fuel injected bikes. Its much easier to fix the lean and rich spots with a fuel injected bike than it is with a carb. You can do it with a carbed bike, but its going to take a long time and someone who knows those carbs really well. And those people are getting harder to find.
As far as the sync goes. Carbs rarely go out of sync. at least out of sync to the point of needing adjustment. But, who knows what has been done to the bike before you aquired it. Out of sync carbs will run rough down low and clear up at the higher rpms. They will also have a very erratic idle. Also, if you rev the bike, the rpms will generally come back to around 3-4000 rpms quickly. but then drop very slowly back to idle from there.