After seeing the damage to the reduction gear caused by the worn-out starter, and watching (and listening to) the first video several times, I don't think I would bother with pulling the rotor. You may want to check the starter clutch by turning the big gear a few degrees clockwise, then turn it counter-clockwise to feel how it locks up. Do this over at least one full turn of the gear, and also inspect the teeth for damage, in case one of the broken teeth got caught in between the two gears.
When you remove the chain tension-er, have the motor in the position where you set the tension. Also, while you have it off, make sure the plunger moves freely with the set bolt backed off: the spring should push it out.