I found a pin spanner that could be bent to size. Good enough to snug the collet. Yes, here are flats for a wrench on the spindle, which is another option. (Whoops, I forgot about that, because I had earlier dismissed using it when I needed pulling so hard on the collet that I risked destroying the threads.) Now, that the collet works as it should, the flats are another option. This problem is solved.
There is a 4-step pulley on the motor and one pulley on the spindle.
I'm settling into my K3 with a handsome built-in router, which is a still a nice setup. The only lingering problem is getting the the router to raise and lower easily. I must be overlooking something or there's grime in the sleeve that will eventually give up after a couple cans of WD40.