If the bow is F/F approved, maybe try a nice skinny string w/padded loops.
A Stringfollow Hill Longbow, pick a shaft any shaft they are hush hush. Have'nt tried'em with a skinny string yet. Mine even with 18strand FF and 8gpp arrows is very quiet, the dacron string just makes a lower tone. Backset ones have little more tension at brace height so the string may be ever so slightly higher pitched, still pretty quiet though, and, plenty quiet in my book. Of course the above setups do not wear ANY string silencers! At all! The only noise you'll get with a tuned Hill bow is the feathers going past the tiny riser.