My two cents:
You might want to check with another doctor. I have scoliosis and grew up weak and thin. Years ago went to an orthopedic doctor who put me on a set of rehab exercises. They helped strengthen my core and gave me a good start on a strong back.
However, I haven't had degenerating discs. Does the doc know what's causing that? Is there any way to address it other than painkillers?
The fact that you're overweight suggests 1: you already have a big load on your spine 2: diet probably is out of whack. My suggestion is to get your food under control. Keep protein up and carbs moderate. Shed some pounds, you'll feel way better.
If your spine stays the way it is, then there are options other than deads. Lat pulldowns, hyperextensions, rows, reverse hypers don't put the same stresses on the back as deads. Try and find a doc who knows sports medicine to figure out what will work.