Your clarification of speaker type would certainly support your complaint. In addition to my comments about how to handle the problem if the speakers were front firing cone/boxes, consider that the back wave of the speaker needs to be hitting a surface which has a diffusive nature AND optimally should be at least 5 ft from that surface(wall).
Now you have to consider the off axis radiation pattern of the back wave from the ribbon which may be strong enuf to cause a delayed bounce off the screen and muddy up the imaging/high frequencies.
The first thing that comes to mind is that your speakers are too close to the screen, laterally speaking. If you can increase the distance between your speakers until the distance between them and your sweet spot (Chair) creates an equallateral triangle. That way you will minimize the level of off axis tweeter strength. That might be enuf (assuming you treat the rear wall).
Another solution (from someone who doesn't think much about the benefits of a back wave, and prefers pin point imaging from front firing drivers (I've had electrostats & panels, but never ribbons) because while bi-directional speakers, omni's, etc all can create the impression of a huge sound stage, normally that comes at the expense of pin point imaging which suffers. Try placing some light material over the rear of the tweeter. This will not only reduce output which will hit the screen it will also solve some problems with the back wave off the wall. Initially use something really heavy so you will hear a dramatic difference and then start reducing the density of the materiel 'til it sounds right.
Or just cover the screen with something pretty that you can simply remove, fold and put away when you are not listening to music critically.
BTW, it would be helpful, and save a lot of collective effort, if we knew what speakers you were using and what the dimensions of your present set up are. Lot of guessing going on here. :-)
