Here is some reading for you on batteries, may help you determine the shape of yours, look at the charge tables. But 12.6 sounds right,should be more for a Gel battery at full charge.
All in there:
However it depends when you do the test, you have to wait for the surface charges to dissipate first or turn the lights on for a minute then wait 5 minutes or so to accurately gauge the Voltage. Clymer says wait 30 minutes after charging to test the Voltage.
Alternator seems OK at that voltage but you'd need a shop manual to test it properly.
What I would do is to connect another battery to the bike,with yours fully charged first, as in jumpstart from another vehicle. If it is still sluggish, I'd suspect the starter.Check all the connections first including the one at the starter and the ones next to the fuses, the starter wire is connected there too.
But if it is the starter, let me know I have a way to remove it without tearing half the bike apart or cutting anything. I just haven't had a chance to post it yet with pics.
Do not insist too much on a sluggish starter, it may only need a cleaning and new brushes, if you hold it too long you will burn it!