Another good idea would be to get something like the Hondamatic that I have been trying to find a buyer for ($1,500) which leaves plenty of cash for modifications.
You did not say how much one arm is shorter than the other. I have one arm 2" shorter than the other and have ridden with unmodified bars. If your asymetry is greater than that, you could have the bars modified with a simple solution that my wife had on her Triumph.
She found the reach to both bars was to long for comfort. A local machinist cut the bars about half the out from center on both sides and made set back brackets for each side. What she ended up with were nice sturdy 2" thick flat sided metal bars with a round opening at each end for the handlebar ends to fit through. Below is one of my crude unprofessional drawings. It shows the design of the set back bracket and how the two cut ends fit into the bracket to create the set back. In this drawing the bracket has been fitted to the right handlebar, with the rider facing the left edge of the picture. Just flip it over and you have the left handed unit.
Not shown in the drawing are angled cuts in the ends of the brackets, with threads allowing Allen headed bolts to tighten the grip on the handlebar ends, after they are inserted into the bracket openings. I am not sure how to show that in a drawing but any machinist will understand what I mean by this.
While my wife had this done to both sides, I don't see any reason it could not be on just one side, to compensate for a shorter arm.
You need to be sure to cut the bar such that you leave enough length on the hand grip end to mount any controls you will operate with that hand.Don
