Can anyone recommend a slinging style for a guy with glass shoulders and back problems?

don't know about the severity of your problems, ask a doctor for better advice.

recommended sling style would be underhand (not balearic).
i never sling if i have an unknown pain .
but i sometimes have noisy shoulder(without pain), at such circumstance i warm up better and sling with much less power.

if you believe it's gonna hurt you then it's gonna hurt you.(do what you love and love what you do.)

most pains and injuries i had was due to muscle imbalance.
for example too strong biceps in comparison to the other muscles around shoulder capsule created sounds and some times pain.

see what baseball pitchers do and why , criticizing for techniques (inverted-w). they have done a lot of research....

underarm.
Effective, good for most slinging situations and you can just use your wrist.

You just have the arm and sling hanging down and just spin the sling in  a vertical rotation with your wrist.


So style one at beginning of the video, but instead of rotating your whole arm. just use the wrist and elbow.
Old video, haven't needed an elbow bandage for a long time.  Did more sidearm back then.

I concur. From time to time my shoulder hurts. Underharm causes the least amount of shoulder stress. For me personally it is the most accurate form also.