I use left hand to open/close the clamp
Generally if you are right-handed you will hold the pole on the right side of the body and use your left hand to open the clamps.
If you are left-handed you would usually hold the pole of the left-hand side of the body and use your right hand to operate the clamps.
In either case you would use the thumb of the operating hand to either pull open the lever (LH use for RH people) or push open the lever (RH use for LH people). There should be no need to have the clamps on the under-side for this to work.
These clamps have been in use now for nearly 5 years and we count many LH users as our clients. In fact my father who has helped in the development and testing of these clamps is left-handed and has been using these clamps daily for all of this time. Perhaps I should get a video done showing how he operates the pole/clamps as a LH user - would this be helpful?