Lots of other people fly at the same location with a variety of
equipement with no trouble. I've flown a variety of different gliders
there with my old transmitter and never had a problem. I really don't
think there's a conflicting 72 MHz signal.

It really is just this transmitter at this particular site - other
transmitters at the same site are fine, and this transmitter at other
sites is just fine.

Is there any way to make this work?

You didn't say, but if that "military site" is an airport, there's a
localizer beacon that's probably just off the end of the runway and is on 75
MHz. Could readily be strong enough to give your receiver trouble.

W4ZCB