Sorry - no experience here with one-handed braking.
But, keep on trying and hopefully you'll find something that works for you!!
Perhaps a coaster brake of some sort?
Or, maybe a 3-wheeled recumbent (2 wheels in front) would work better? This would take the balance issue out of the equation - perhaps there is a foot-actuated brake for recumbents.. ? I've seen some pretty racy 3 wheeled recumbents online.
Best of luck!