I've used my trolling motor and a paddle to get home from far away more than once. Caught a few fish along the way too since things weren't happening to quickly...if you know what I mean.
It pays to keep that deep cycle fresh!
I suspect your problem will need the boat running at 5k in gear to duplicate the harmonics. Just can't do that in the driveway. But, from what you initially described, it should happen, if it's going to, pretty quickly don't you think?
Here's wishing you luck.
Keep us posted.
PS As I was re-reading your original post, it struck me that you say "once I throttled back". It reminded me of a Pontoon my customer had that kept being a phantom problem requiring "rescue" from the rental center. The responding dock hands always came back saying they could find nothing wrong and the boat ran perfectly for them. I finally found the solution to that one in the shifter handle where a wire had rubbed through. Electrical tape and no more rescues. Just a thought.