OK. So, this does not look like an electrical issue, and looks more like fuel/air issue. Very puzzling. It's probably better wait for someone more knowledgable. However, it's always a good idea to eliminate simple things first. Try disconnecting PC, and see if this helps. Try putting '87 octane. When was the last time you looked at the plugs and they looked good? Also, did this problem progressed gradually, or appeared all of a sudden?
I bet the issue is present in 1st and 2nd, just not noticeable by the feel. The fact that it gets worse with higher gear because the taller the gear the more "difficult" for the engine is to pull the bike, so the same problem simply gets amplified.
Try gradually rising rpm while idling. Is there a hesitation at about the same rpm?
Another simple thing to check: lift the tank and check all air/fuel hoses carefully just to exclude the possibility of air leak, etc. See if any oil/sludge got on any electrical connectors.
Another crazy possibility is that at a certain rpm, a bad electrical connection somewhere gets worse because the connector resonates on the frequency at a certain rpm.
Otherwise, I'd suspect a map, plugs, injectors - not too sure though.
Another easy experiment. Put the bike on the rear stand, start up, and put in 3rd gear. See if that happens. If it doesn't happen while bike is on the stand, but does happen when you ride, then it's definitely fuel related because without the load the engine needs much less fuel to sustain the same rpm. So, if it's a fuel, again points to map, injectors, sparkplugs, maybe even fuel pump.
I jest re-read your original post and noticed important detail - you say it happens when you get on it hard. While you have the tank up, carefully examine your throttle cables for a possibility that there is some sort of binding which simply delays the cable movement. When was the last time you lubricated your throttle cable?
Try simple things first. There was a post recently how someone's idle became too high. In the end, it turned out a piece of something stuck on the throttle stop screw - all it took was a carefull look under the tank.