It looks like you ended up posting this twice, so, since there are no substantive (sorry Oscar) posts on the other version, I'll delete it.
Degeneration at 53 isn't really "early". You have a kind doctor who was trying not to tell you that you are getting old. The usual age for onset of osteoarthritis is around 50. Or maybe he or she meant "still mild" degenerative changes. If so, good.
Yeah. Traditional hyperextensions aren't the way to go. You should not be moving a loaded lumbar spine. You need to train to stabilize it. This means isometric exercises that train the muscles around your lumbar spine to resist movement and thus to protect the spine. So exercises like planks, Pallof "presses" are good. Glute bridges require you to hold your lower back in position, so they would be OK if you are careful that the movement comes from your hips, not from your lumbar spine. You can do a modified "hyperextension" that really only goes from slightly flexed to neutral, not into extension. You can do that off the end of a bench, or at many commercial gyms that have a hyperextension bench. You can train your hips and thoracic spine for mobility, but your lumbar spine for stability. Twisting at the lumbar level should be avoided. No situps or traditional crunches. Look up something called "McGill curlups", or "McGill crunches". http://www.youtube.com/watch?v=Ey9uiWiiL6I