Thanks Steve!
The hook shaft play seems reasonable but I'm basing that on a Singer. I'll check it again. I do notice that moving the hook shaft to both "extremes" of its play doesn't seem to affect the hook's positioning but maybe it's just that minute.
The hook mount is a heck of an idea! I haven't seen the set screws for it - which might be why I didn't think of it - but I will look harder momentarily.
I think I was working my way to a scenario where something had to change tolerances as the sewing went on, but I hadn't thought "warmth" would be an issue in something so loose.
I will test and report back!