One of the fans I bought is controlled by a remote. In the normal base,
the receive would slide in and get covered. Unfortunately, I had to
install on a sloped ceiling, and couldn't use that base. I have a
rectangular hole in the wall from an existing fixture, and I was
planning to mount it there somehow.

My first effort was with just some velcro tape, but then the receiver
wasn't flush against the wall, nor did it hold for very long. Is there
some kind of box I can mount these things in? I'm assuming they aren't
standard in any way, and I'm just going to have to make something up.

A multi-ganged light switch box should work. Not sure if it would fit in a
3-position, if not, go to 4. Might be hard to find a blank cover of that
size, but some places sell the type that come in multiple pieces and you put
together the type of cover you want...

-Tim