OK, well, when flipping just flip however much line you can dangle, but use the longest rod you have for more reach. You just want the bait to swing out and land softly like a real bug or critter just fluffing the water surface. I flip with both hands, whichever is handier, right hand when on the right (starboard) side of the boat, left hand on the other (port). The reel should be locked down so the spool can't revolve after peeling out as much line as you can handle. I can reach target 12-14' away without holding that spare 6' to my side.
If that nerve damage is long term consider buying one really nice reel with digital backlash control, and practicce using the better hand. They are expensive, but keep you fishing. I had a left-hand retrieve Shimano Calcutta TE DC round baitcast reel last year ($500) that was impossible to backlash. I bought it without my wife knowing. She flipped. She knew I was totally satisfied with my Curado 201's, so why do that? I got it to take the occasional client fishing that has no experience. The next client loved it so bought rod and reel for $75 more than I had in it.
Being more realistic, a closed face spinner reel would be a great change for you. Anyone with one hand can use those. Spinning reels would be easier to use than baitcast, having one tired arm. But a good compromise, if wanting to use baitcasters, is to get and learn to use combined magnetic and centrifugal brakes, available on reels starting around $80. Set the magnetic brake (dial on end of reel) to control end-of-cast problems, and the centrifugal brakes (pins undera removable plate) for close up start-of-cast problems. The idea is to go heavy on both, gradually easing off (push in one pin at a time or dial one lower number at a time) until you find the sweet spot for your line and casting style. That, plus easing off on power of cast, ought to eliminate most backlashes.
The spool tension knob needs to be set once on the first lure selection. Don't move it again until switching to a different weight of lure. When properly set the released spool will let the lure slowly drop about a foot a second. Any looser and you will get extra backlashes. Loosening it for a faster drop allows longer casts, but backlashes are not a good compromise, trading efficiency for distance.
Another tip is to never use a shoulder when casting. From start to end of cast your elbows ought not move out of position while at your sides. Using both hands and wrists, with some forearm assist, snap the bait out. Never reach the rod tip behind you for a cast. Snap the rod tip like cracking a whip. Hold it with tip aimed at the target, snap the rod back like lightning, and just as quick snap it forward, ending the cast with tip aimed at target. The thumb does the rest, feathering the cast to a quiet stop. Your arms will last forever doing that.