Like I said, I didn't want you to take that wrong - you sound super strong on the upper body is all, yet you are basically saying this is your weak point...
You are doing squats with 295 it sounds like, and deads with 315 - do you feel any pain when you do these exercises? You are still using a good amount of weight (not on par with your upper body, but still strong) and this weight could cause injury just as easily as 400 pounds or 500 pounds, if your form is in check.
When I was a teenager, I hurt my back playing sports a lot. I was afraid to deadlift heavy or squat heavy, and I kept hurting my back. One day I decided I was going to get these two exercises up, and I started lifting some heavy ass weights. I went from deadlifting 250 to about 400+ pounds and suddenly my back was never hurting anymore. If your doctors have told you to avoid these exercises, then I can't argue with that, but if you are avoiding the weights out of fear, then it is your fear that is causing your pain.
Start comfortable and add a little each weak. Don't go crazy, keep your form in check, and pay attention to pain. Don't be a hero, but don't be afraid.
Finally, one thing I really like doing is pre-exhausting before deads and squats. I feel it allows me to work with heavy weights, get more impact, and improve safety. The flip side is that it can be very taxing.
I do heavy leg-extensions and then superset with squats, taking both to failure - no rest. It is taxing. Sometimes I do a drop set on either the squats or the leg extensions. It can be brutal.
On back day, I do hyper extensions with weight across my chest to failure, then superset with deadlifts to failure. Again, I may incorporate drop sets.
The other thing I have to say - when I was younger I lifted explosively, since returning to the weights a year ago I started following a slower, more controlled pattern that takes me 3-4 seconds up, pauses in the contracted position for 2 seconds, and then 4 seconds down. I had to check my ego at first and drop the weights to accomplish this, but it works and I can tell you that I had minor shoulder injuries with nagging joint pain in my left shoulder in particular, that has completely disappeared and I credit this controlled lifting with that. My muscles got stronger, but weren't being tugged and I had to have more control over the weight.
If you simply cannot do the exercises because of the surgeries, that is a different story, but that doesn't sound like it is the case. Be careful, but don't be afraid!