incline bench as steep as you can without pain seems to be the only real replacement for the press.
Have you tried different hand positions? ie dumbell press with your hands either neutral or supinated instead of the standard pronated grip?
If none of the press grip variations work, you might want to just try plate raises, lateral raises. In other words, pick some shoulder and tricep exercises that would normally be considered "accessory" lifts, and do them as main lifts with the 5/3/1 schema (heh heh, i said schema).
The important thing is to find exercises that work that joint without pain.
Is it an option for you to strengthen your back? I have zero experience/knowledge of back injuries, so I'm just asking