If they were mine, the first thing I would do in an attempt to improve the sound would be to find some way to brace the frame against fore and aft movement, like a strut from the middle of the frame to some solid object behind the speaker, ideally the floor/wall junction, if feasible. I'd do it in a temporary fashion to test the result—a well placed broomstick or two (or equivalent) would work as a test of concept.
Every time is see a lightweight planar speaker I think of the effect of that large diaphragm, well-coupled to the air mass in contact with it, pushing against all that air and being resisted by so little mass in the frame.
I would be interested in hearing from you about the results if you try this.