. . . simple test would be to dampen that hypothetical "ringing" by just placing your index finger vertically against the middle of the grill over each ear while listening. When I do that, it seems to however have no effect on the sound in that range of frequencies.
Yes and no!
With open back headphones like Edition and even Sundara, placing anything near the back of the headphones can make audible changes to the sound ( back radiation), one extreme case to make my point is, with your palms flat out, bring them close to the back of the earcups, even without touching the grill, you hear a change in sound as you get closer, changing the angle of your palms makes weird changes too.
The dampening of the bars
is the way, but not with your fingers! hence my suggestion with gel tape.
A narrow gel tape, if stuck to the centre of the bars can take the edge from the (alleged) ringing phenomena. It won't fully dampen the bars, but tames them down. while being soft and narrow, its effect on the back radiation should be small.
A better way is to find two lollipop sticks (round cardboard ones), stick a very narrow gel tape on it length-wise, then stick it to the back on the grills vertically, making sure the top and bottom of the stick dont peel off, as the grills are slightly bowed outwards.
This makes a good damper, cardboard stick doesn't vibrate and the tape sticks the grill bars. Also the roundness of the stick means little interference with back radiation.
Costs nothing, but a little time and it may be fun.
IF it bears results, then something permanent can be done, otherwise, remove it, no harm done.