I gave up on this for a while, then today I was reading about RF module usage in general, and learned that the process is more complicated than just streaming bytes into the slave. The timing of SS changes is important because it delineates messages of multiple bytes. I think I really need to get a datasheet for this module if I'm to get anything done with it.
So this forum is probably not the best place for my next question, but I'll put it here anyway to keep this little story going... I searched all over the net for any clues about the identity of this RF module, but couldn't find anything. Maybe somebody more experienced would have a better clue about identifying it. The printed text on the board appears to say:
BTL-RFF0-01 V1.4 HJ29A94V8
2013 9 16
4013
... but as you can see, some of it is a bit unclear:
On the RF chip itself, the printing is much clearer but far too small to take a photo of (with any camera that I have at least). It says:
2402E
5325.1
AD1311
If anybody has a better suggestion for a forum to ask this in, please let me know.