Spy/Crime gives a lot to work with. Hot Moon brings in the USAF space spooks from the planned Blue Gemini program.
From actual history, there are great nuggets popping up in Harvey's Soviet and Russian Lunar Exploration book.
The Russians didn't have radiation hardened film for the cameras they sent to the moon — but US spy balloons had that sort of film, and we were delivering it right over them!
In 1959, a few months after the Soviet launch of the first Automatic Interplanetary Station, Ye-2a (later branded Luna 2 in 1963), they sent a mock-up to an exhibition in Mexico. Turns out they sent a fully functioning back-up unit. With a nod from Mexico, the CIA intercepted it and managed a couple of hours of study before sending it back along its way.
In spycraft adjacent activity, Jodrell Bank Observatory was monitoring transmissions from Luna 9 in January 1966. When the transmission sounds changed, the PR officer recognised the sound of the fax machine used in newspaper offices. They scurried off to the Manchester Daily Express, brought the fax machine back to the observatory and scooped the first photos being sent direct from the surface of the Moon. Nikita was not amused.
Another good alt-history take would be if Kennedy survived and went on to develop a joint lunar landing with Moscow. There had been preliminary flirtings of such a plan, but Johnson would have none of it. If that had gone forward, there would of course be endless spy vs. spy activity all along.
Moon Zero Two does a nice start on the crime angle. A motion for more moon crimes is always in order.