I don't know of any 20ga loads, in 3/4 oz, that are published for Universal. Hodgdon website lists International, Super Hcp, and IMR's PB. So I was experimenting with International ...but it has a snappy recoil to it.
I use a lot of Hodgdon Universal in my handgun loads from 9mm - up to .44 mag ) ...and I've traditionally used it in 20ga 7/8 oz loads and 3/4 oz loads in 28ga....
To the OP's point about shoulder issues ( my shooting shoulder has been completely rebuilt...including having the bicep cut and shortened ) so I feel his issues every day ....and although after the surgery I'm better / its still not as good as when we were young.../ but a combination of things ....if you want to fire a fixed breech gun ( pump gun, O/U or SXS ) then you need to go to a heavier gun ( maybe 8.5 lbs ) and keep the payload on shells in 12ga no heavier than 1 oz ...and velocity at or under 1200 fps.
For many years...my primary shell in a 12ga was 1 oz, 8's, at 1225 fps...and on days when my shoulder was bad.....I'd go with a Benelli semi-auto with the comfort tech system in it....or I'd go with a gas operated semi-auto like one of the Beretta's or Browning (Maxus, Silver, etc..).
If I wanted a "Tactical" fighting shotgun....I'd go with the Benelli M-4 because its gas operated. I sure wouldn't beat myself up with a pump gun.
I shoot pump guns a little - for fun - Browning BPS hunter models 28" barrel...but I keep the loads real light.
If I just have to shoot an O/U on bad shoulder days....I reach for my 28ga Browning Citori XS Skeet model, 30" barrels, about 7.5 lbs ( it was built on the 20ga frame ) or my .410 ( in same configuration). Beating yourself up ...and eating 7 or 8 advil all the time...is not a good idea !!
This stuff is supposed to be fun !