Yes, The hinge should be on the small string side. <
With dense foam it wouldn't seem like any vibrations would cross to the other strings. It shouldn't be that hard to quickly make a working prototype to prove wether it does or not.
I understand the reasoning here - seems logical. Initially, I did not consider the difference in pressure across the strings.
When I tested the foam sandwich it actually seemed like the smaller (tighter, more pressure) side might be better on the fatter strings, because they required more pressure on them to have the same dampening effect. This is kind of counterintuitive at first, but I think it's going to require some testing to find the best result.
Amazing feedback here - 20+ minds are better than 1!