The problem you described are either carb related or ignition related. (Supposing valve clearance, etc. is good, I'm not sure what has been done already.)
Regarding the carb, since you suspect the PO of having changed things, maybe the jetting/anything else is changed as well as eldar already suggested?
The pilot screw is located at the engine side of the float chamber (see arrow in pic)


The upper pic is from the "Honda Technical Manual on Motorcycle Carburetion" which is mentioned and linked to in the carb faq, a good read btw.
For setup you screw in clockwise until a
slight resistance is felt. STOP!! Then you simply screw it out again to a certain number of turns given by the manufacturer.
The workshop manual tells about a hundred times (so they are really serious about it) to be careful when screwing the pilot in, as its seat can easily be damaged.
There might be some kind of security cap over the pilot, now if that's the case I would forget about the pilot since its setting is stock anyway, which is what you (at least initially) want.
If the carb identifies itself on its side as a VB 54C or D, the pilot setting is 1.75 turns out. Mainjet #98
If the carb identifies itself on its side as a VB 54E or B, the pilot setting is 2.625 turns out. Mainjet #95
Now, hmm, the thing is I don't really think it won't help a bit. I'm smelling a problem with the ignition (gets worse when warm, doesnt rev over 5K) but then again this is maybe because I know the cb 650 ignition inside out and have only limited knowledge with carbs....do you have a timing light?