In looking an an old HT carb it would seem doable....would require drilling a hole on the other side and rigging up a nut and bolt setup to hold the lever and choke plate all together....I do see that the there is a flat spot on both sides that is cast into the carb where the factory pieces are located but I suppose with some precision dremelling maybe some small washers could be fabbed to make a flat spot for everything to mount to (of course it should be sealed to prevent additional air leaks....
I thinking about it, while it does seem easy in theory, I can see it being somewhat time consuming...If the cable choke works I would think that would be faster to do possibly...
Another alternative may be to build an intake that causes the carb to face forward....maybe that would kill 3 birds with one stone in that you could : 1) move the choke to the left side as you wanted 2) Make it possible for "Ram Air" to work since the carb would now be facing forward and 3) if you made the intake the proper length (i.e. a tuned intake) you could see better engine performance....
Since you've already tried the cable choke....maybe one of the other 2 alternatives would be good.
Hope this helps
PS - I personally like the last alternative! ;-)