Probably heresy to a SoCal ocean paddler, but try a single blade craft for the shoulder. A canoe. I've had shoulder issues on and off -- not serious enough for surgery -- and I've noticed the problem is a lot less if I single blade on one side rather than the other. It actually helped me become more ambidextrous as a canoeist.
Using a rudder to avoid correction strain with the paddle makes perfect sense to me.
There are many ruddered outrigger canoes in SoCal, which you can single blade on either side or even double blade if you want to. It may be worth a try to borrow one.
I also noticed that soft catch paddles helped my shoulder. Round them off to get rid of edges or even make them rounded points like some Aleuts.
A flexible shaft also helped me. I can't stand the iron-rigid carbon shafts on some carbon canoe and kayak paddles, but the ZRE flex shaft treats my shoulder and elbow much better. I'm sure there are modern kayak paddles with a variety of shaft flexes.
Classic Freestanding Rack
Touring Kayak Paddles
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