Given the size of the painting and the fact that it will be looked at from a distance, I suspect something like the grommet idea would be strong enough, but you would need many of them to avoid distortion. Other approaches might work – are there any conservators or artists nearby that could help you?
Rolling up the painting repeatedly will eventually cause damage – cracks in the heavy paint and paint flaking. If you give up the idea of moving it, you will have more options for hanging.
Velcro strips that have adhesive on the reverse might work. You can get information from the manufacturer about how much weight it supports so you can figure out how much you would need.