You can mount any shifter backwards, but it may be difficult to use in one direction or the other. Top-mount thumb shifters are probably the easiest. Gripshifters would work also.

Having only a rear brake is the worst possible solution. IT could work ok for a beach or boardwalk cruiser, or maybe a child's bike. But if you ever plan on riding on a road or at a speed of more than 15 kph (10 mph) then it is a bad idea. THe front brake stops you much much faster and with less effort.

Switching to a left-hand-operated-front-brake-only setup makes more sense and solves you bar clutter problem, too.