I wasn't sure what to call it, so I called it a splitter, but I knew that wasn't right. Yes, I'm fairly certain that it's this multiswitch you're talking about. I'll take a picture when I head over to my folks' place later today.

It has 8 outputs, and I believe 7 of them are taken up. At this point in time, the absolute necessary minimum needed would be 4, preferably 5 or 6.

The problem with amplifying before the multiswitch is that it appears that this messes with the main home theater's signal level. Before I was working on all this, I had an unpowered multiswitch (now I know what to call it), and the home theater could get HD channels. I then replaced it with a powered multiswitch with the exact same connections, and this took out HD for the home theater, which is only about 15 feet away from the multiswitch, as opposed to at least 100' for the room in question.

I'd be happy to minimize the number of cables on the output side of the multiswitch, but this raises a problem I've had since starting on this project: it's such a pain to figure out which cable goes where! I can only identify one of the cables going up to the room I'm trying to get signal in. This is frustrating, because in that room, it's double-coax cable, and I can only reliably trace one of them down to the cabling closet in the basement. Argh! I can't stand this...