Please attach a pic of your guitar with the GK3 attached. I've seen a pic on the web (on a Roland site ?) showing this, but this does not seem to bear any relationship with your comments/problems.
Yes, if you are picking up various sorts of non-guitar sounds, and these are being received by the G2M and converted into midi (the G2M would not know any better) then this will be causing major problems.
The pic I refer to above shows the GK3 attached at the very base of the guitar, about as far from the strings, and where your wrist might be, as possible.
Very little of the problems you refer to relate to midi as such. Some are more to do with the mechanics of the pickup, and maybe settings connected with it. Other problems relate to the overall system, the number/complexity of connections between pickup, the converter, cables, computer (performance, drivers, etc).
I would make no comment regarding the relative merits of the Roland or Korg units that are producing the final sound - this is a matter of your taste. I assume that some people DO like the Roland unit?
I'm not sure I believe in this thing called 'latency', I've never experienced it myself. I'm not sure it's anything to do with midi. What I hear about is caused by the complexity of the system as noted above. A faster computer can help, more important will be to make sure that your computer is doing NOTHING ELSE other than processing your music data, yes, I know that this is a BIG problem for WinDoze, which seems to be OFTEN inclined to do other things as well, whether you want it or not, but that's WinDoze for you.
I suspect that you could improve things a lot by sorting out the problems with the initial pickup (that produces the initial data) and then sorting any problems with the overall system (incl the PC).
Oh, just an aside, but I'm in the UK as well. Makes a difference regarding the timing of messages and replies.
Another aside, long ago I got a Roland CP-40 unit to experiment with, I was using a mic for input but I think you could plug a guitar into it. Yes, it worked. It produced midi data from the noises I was making, but it was too prone to make too much data, and really the data produced needed a LOT of work afterwards. I assume the extra noises you refer to are causing you similar problems?
Geoff