I have a build to do this summer where I have the same problem, and my thought was the same as yours - a rotisserie. Something to screw into the end where the strap hanger will go, then some way of holding the headstock end.
I'd like to have the thing presented to me as parallel to my spray gun as possible, so I was thinking the headstock end might have a bit of a wheel affair, where the headstock gets mounted using one of the tuner holes, but offset from the center of the wheel. The wheel's center would be the axle point, with the attachment orbiting that. The thing would probably never balance right, so then maybe some notches or something around the outside of the wheel to lock it in place at various positions.
Could probably do the whole thing with a couple 2x4s and some bolts/tubes. Wouldn't need to be too fancy, as it's unlikely to be reused, or at least not much, so maybe consider it a disposable jig.
I don't know. Just spitballing, not in any hurry. Like to get it done this year, but if not, well, it won't be the first guitar to take several years to get strung up :laughing7:
I haven't been able to find anything online. Most people hang the guitar for this sort of work. If you come up with something that works, I know I'd love to see pics of it here.