After trying the advice we got from the propane service person (not the one at the place where we normally buy our propane) about connecting our RV fittings to the larger bottle (it did not work; there was still a tiny leak so we disconnected the bottle and set it aside) and then comparing it to some research I did online about the POL and ACME gas fittings, we concluded that the advice was wrong. Just telling us "use a large crescent wrench to tighten it down so tightly that you can't get it back off again" is roughly equivalent to saying, "just hit things with a hammer until they start working again."
Anyway, we appear to have identified the adapter part necessary to connect a POL (large bottle) female outlet to a POL (RV/small bottle) male connector. This is good because we'd be out a couple hundred dollars otherwise and be stuck with a bottle of propane we couldn't use.
I was amused to discover that one of the two standards for connecting propane bottles is called ACME. Surprisingly, it's the newer of the two, not one that was deprecated due to unfortunate incidents with a coyote.