I'd guess the problem is more down to voltage drop caused by the headlight (if I'm right in thinking that's lit all the time when the ignition's on).Or a duff battery.
What's the actual voltage measurement across the terminals?
I'd expect the battery volts to take a bit of a hit while the starter is cranking the engine over, but as soon as the engine's running under its own power the voltage should be back up.
The starter motor ought not to be drawing anything once your finger's off the button.
If you've a voltage of 10v once the engine is running it still points to a duff charging circuit
I still think its your stator running hot
I'd be more suspicious of the sparks.
Mine unscrew and I'm fairly sure they all do.
If they're old, change the spark plugs for a new set. one less thing to worry about, and its a lot more likely its them than your coils!
On a secondary note, you can't test a battery for its voltage immediately after charging - they hold a surface charge which goes after a few hours, meaning if you check it originally it'll look much higher than it is
If I understand your issue , you are not getting enough current to both start and charge
... I checked the voltage and it was 12.5 after one attempt at starting which then dropped down to about 7.9 on the second try!!As mentioned, the battery has been on-load drop-tested by Vernon's in Portsmouth who confirmed it was ok.
The battery ought to survive at least 30 seconds of cranking the engine over before it sinks that low. Either it's not getting charged or is duff or, as you suggest, the starter is drawing more current than it should. Seems like an odd fault, but hopefully it's as easy a task to swap as it is on the original Fazer.
Though... if you need to take the rad off the FZ6 to change the plugs, replacing the starter is probably an engine-out job.