You could just replacce the dish with one that has four plugs on it...
Thanks, Tony, but I should also mention that money is a little bit of an object, and this is most definitely not something I can do myself. We'd need that 3rd party installer to come out, get on the roof and up the chimney to the very tall pole the dish is on, and run the new cables across the back of the 35"+ high roof. That's a little out of the price range at this moment

I've tried those in the past with no success. I might give them a try again, but they come in different varieties and I'm not sure which one would work best.
It seems anything that can covert HDTV signal output to run over coax is very expensive.
My hope was that I would be able to find an HD DVR with a coax output, but it looks like DirecTV doesn't offer that on their receivers anymore. Their older ones did. That way I could put the box in the basement where it could get a good signal, and figure out another way to control it remotely, either with some IR solutions or RF. The newest DirecTV receiver appears to have RF built in, but has no coax out, so I'd have to look for a very expensive solution like the one you proposed.
Thanks for the help though, guys. I really appreciate it. Hopefully I'll be able to figure this one out and quickly.