So as I had to re-jet the carbs anyway after removing all those extra baffles in the exhaust, the way was clear to get to that starter.
Getting the starter out is really just a matter of undoing the two bolts holding it down in the back and then pulling it to the right and wiggling it upwards ever so gently, without breaking the cases. But it's pretty clear to see, the bike this engine came out of, was parked outside for ages. So a bit of extra cleanup (and paint) was due.
With the starter clamped into the vice, it was time to undo the two long bolts holding the complete assembly together. Stock starters usually sport philipps-head, whereas aftermarket ones generally have hex-head-bolts holding them together (which makes disassembly a lot easier).
The first find was a completely dry set of planetary gears.
And already the first sighting of a lot of carbon dust, which had found its way past the shaft (no grease of any sorts as well) and into the gear housing.
And wow: Never seen that much carbon dust in a starter and it still working.
The picture doesn't do it even remotely justice on just how much dust had come out when cleaning.
With all parts cleaned and greased (incl. the terminal for corrosion prevention), assembly was a matter of minutes.
It admittedly doesn't sound much different, but now the bike can be started more than three times in a row without the battery breaking down, which I do consider a vast improvement.