Hmm... I see your problem.
This would go a lot easier if you had a reusable piece of thin pre-checkered material that you could just lay on top of the flat surfaces.
Or a LARGE amount of checker-holed tape that you could just cut out pieces of it as needed.
maybe this exists? Or maybe it can be produced? If it saves you 100 hours of painting time, that's gotta be worth investigating..