Before we knew better the answer would be sheet lead. (the metal)
Because we know lead is toxic and causes brain damage, and through the wonders of modern science (!) we have high-density polymeric rubber
The Auto dudes call it "Dynamat" after the big brand name player.
It comes in many thicknesses, some offering heat insulation to car firewalls and floorboards, so choose wisely.
Better yet, stop by a higher-end auto stereo installer and ask for a scrap-end.
Polyurethane insulating foam also comes to mind, but it expands and is harder to control.
The 800hz peak is not unusual in a Comm mic, because that emphasis increases intelligibility.
About interfacing mics to your UHF radio, there are a few project boxes out there.
The challenges are RF getting into a hi-fi mic as well as type, level, and impedance matching.
Remember that Dynamic Mics are inherently more RF resistant than Electrostatic, which need power back and often Mic circuitry and pre-amp.
Ferrite beads and Faraday shielding may be adequate RF chokes, these are chosen by frequency, an easy choice when comparing 50+ MHz RF vs. 200Hz to 8Khz communication-intelligible audio.
The home brewers way was often to use an interface testbox or ugly-board and when a solid solution revealed itself, to miniaturize perhaps to get the needed interface into the mic case.
Good Luck !
(FWIW, I am strictly CW-QRP, and mostly inactive, but the SDR has brought me back into the shack...)