Ron,
I am not an expert in medical manners, however one thing which would be worth a serious try is to send with your left hand. I am 80 years old and very right handed. Perhaps 7 years ago I had a serious injury to my right wrist/hand which required sugery and about 3 months of physical therapy and recovery. I was very surprised to find out that I could accomplish many, or even most chores around my shop and house with my left hand. It was mentally exhausting, but the human body adapted to this challenge. Since I hoped for recovery, I never worked on left handed CW, but am sure that I could have mastered it with some serious effort. It was common in the old days for contest operators to learn to write, or usually send CW with their other hand so they could write with the other hand. One friend always sent cw with a hand key with one hand and with a bug on the other. Even though I am now completely recovered, I now am just as likely to pick up a coffee cup or coffee pot with my left hand.
One other thing you could try is to set up, or get a key with wide spaced contacts and perhaps stiff springs. I operated many years with hand keys, bugs, and heavy clunky paddles which I needed to really bang hard. Recently I finally bought a quality (expensive) key which required a light touch. It took this old guy some real effort to learn to control it compared to my old Kent and some hand built keys. Possibly something like this would be easier to control.
So just keep experimenting, something may help you. Some folks claim that some rigs or keyers require more exact operation to send good CW. Personally, I find all of my rigs and keyers OK, but I seem to still just adapt to whatever is required, but I would try different keyers or rigs with internal keyers. I think the idea of a single lever paddle should be in theory, easier to control. Iambic squeeze keying is probably the most difficult to learn or control. Many decades ago I built my own discrete component keyer which was similar to what is now called Ultamatic. It was very easy for me to master, and I was soon cruising at well over 40 WPM, which I never mastered with all of my fancy "modern" keys and keyers. Some keyers still offer Ultimatic as an option. Will not solve your problem, but may help just a bit if you want to stay with dual lever paddles. Good Luck Rick KL7CW