You should really find a jazz bass that fits you in my opinion. As we get older our bodies change and being able to handle the load is one of the abilities that diminish too. I'm not sure how many headless jazz basses are out there but a medium / short scale would be an option too. Sire offers a short scale PJ and there are others for sure.
Getting and staying in shape is a good advice but I wouldn't expect this to solve the issue. Anyhow, the muscles that do the most work in this case are you upper back and shoulder muscles (trapezius and deltoids) so push-ups (while a great al around exercise) are not a good specific exercise in this case.
Getting and staying in shape is a good advice but I wouldn't expect this to solve the issue. Anyhow, the muscles that do the most work in this case are you upper back and shoulder muscles (trapezius and deltoids) so push-ups (while a great al around exercise) are not a good specific exercise in this case.

