My intake rubbers are cracked and were when I bought them. They had electrical tape covering the cracks and I never took it off and have covered some 20,000miles with them like this. However, the other day I decided to sort them out, so I removed the tape and when ridden it behaved very similar to the way you decribe, once you reach about 4,000rpm it become very sluggish and when you open the throttle in bogs down and sometimes dies. I have now replaced the tape and I'm looking for some replacement rubbers (£90 new). Looks like a bit of a job to change them though, I need to see how many bits and pieces I need to remove and how much I can moved the carb back in order to remove the rubbers.
I had one of my carb rubbers fitted incorrectly before (folded in on itself) and as you say if there's an air leak then the bike will bog down and ride really ropey on acceleration.
I noticed the OP has said the bike won't even think about starting with the choke on, which would suggest it needs either more air, or less fuel.
The backfiring on overrun would also suggest unburnt fuel as well, so same scenario again, too much fuel or not enough air.
Air filter would be an obvious start, but do not get a cheapo one, get either K&N or an OEM one, whatever takes your fancy.
I bought a cheap Hi-Flo air filter before and it felt as if the paper was double the thickness, it was really noticeable to ride, so i binned it very quickly and replaced it with a K&N which was like feeding the bike a packet of Fisherman's Friends, i could feel the bike thanking me.
If that doesn't do the trick then i'd guess you have a problem somewhere within the carbs.