I Use the Rift-S.
I had the same problem with Challenges sound pack when removing the headset. I solved this by putting a small piece of cardboard over the sensor (in the headset just above the nose) when playing AH (honestly i just leave it there).
This way the Headset doesn't know it's been removed.
The problem with loosing game sound lies somewhere in the transition from "In Headset" to "On Monitor". This may be solved or alleviated also by setting ALL SOUND SOURCES the same from "desktop to game to Headset source settings".
Alas, that is a pain in the bellybutton to switch n set every time you wanna play AH, so just use the stupid teeny piece of cardboard.
P.S.
I also have the P-51 experience, however it doesn't seem to be "every time" and I also have gotten use to it. It's actually Kind of nice knowing what it is and the I need to do some Pilot Stuff when I hear that all of a sudden behind me.
Good luck,
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