Long story short: it was a bad motor. All voltage tests were more or less good. The new one is nice and quiet. And expensive.
There were some issues regarding the install that I'd like to detail in another post. Last year the slide was damaged somewhat due to an obstruction that prevented the slide from extending fully. This actually bent the plate upon which the slide motor was bolted, it seems. This, in turn, added a lot of extra stress to the motor, already a veteran of over 100k miles and ten years.
I have pictures and a blog-post coming soon to help others in this situation, I hope.
Until then, thanks to all the incredibly helpful people on this forum.