I took a closer look today and here's what I saw at the driveshaft - reduction gear.
https://www.youtube.com/watch?v=8Q5CjhtAKuU
That doesn't look wonderful to me.
Do you think it's just a worn pin? Or is it possible that the hole in the shaft is worn enough to cause that kind of slop?
Also, the movement on the input gear collar thing seems a little excessive too.
There's quite a mat of debris on top of the gearbox. I definitely need to clean that off.
Thanks again for all the input!