Thank you for your reply! Here are my toughts for your points:
1., 3., 6. The membrane resistance should be low, but not very low: only a few mA has to move in every direction of the membran permitter.
(Lower signal voltage on the membrane decreasing the required current even more!)
So a very thin gold coating for example should be more than enough (I know gold is heavy, but we need only a few nm thickness).
Since I do not have vacuum chamber at home to make such coating, "Emergency Mylar Thermal Blankets" could be a good first try.
It is 12um, which is 3x thicker than ideal, but still close to the target.
2., 5. Four layer PCB (FR4) could be used with copper only on the middle layers and with no galvanization in the grid holes.
Biger spacing is not a problem, can be compensated with even higher bias voltage, which is easy to provide (only a few diodes and capacitors needed on AC).
(This isolation on the inner side will protect the membrane driving transistors too.)
((Instead of FR4 an isolated + tensioned wire mesh could also be used, but I have no ide how to make it.))
4. In case of DC signal or low frequency you are right, the charge goes to the middle, but the charge has to come and go in every period, so on higher frequencies they spend more and more time on the way between the middle and the permitter... Should we also consider "skin effect" on higher frequencies?
7. I think humidity is not good for any electrostats anyway.
8. C = epsilon * A / d, I do not see here problem: the capacity is the same as for any normal electrostat. The good isolator may increase epsilon, bot the bigger distance compensates.
I whish I would have lot of free time to try this concept more seriously.