stuttering fzs 600

[Gnasher]

I've found valve clearances on the FZS600 to be amazingly stable. Check them by all means, but don't be surprised if they're in spec... mine still were at three times that mileage.
Nor would I expect low compression to result in those symptoms:

:agree

  This is either electrical or fuelling, start with the easy things i.e. plugs as already mentioned.  Wait until it's dark or turn out the light in your garage lift the tank and start the bike now look for aching around the top end you may have to move around to see it and check inside the plug wells but it will be obvious. It's a common problem on high mileage bikes replace the cap/lead/plug if they are arching it may be worth changing the plugs as a matter of course and make sure the gap is correct.

If the above is all ok and changing the plugs does nothing start looking at the fuelling begin with obstructions in the air intake, then the filter either clean it or replace it.  Then move to the carbs looking for blocked main jet/s and emulsion tube/s and holed diaphragm/s these can be tiny and will get you the very symptoms you've got.