The SD part is complicated by the fact that SD receivers typically don't offer RF remote. There are third party wireless options for remote control that you'll need to investigate.
The HD part is complicated by the fact that there's currently no affordable way to modulate an HD signal over coax so you have to install some manner of HDMI transmission system (you could use component, but it may not always be available on copy protected content). For my money, the HDMI wall plate setup seems to be the best solution to long-distance HD. It is cheaper than long cables by a wide margin but it requires two dedicated Ethernet cables for each run.
Whether or not RF remotes (DIRECTV or otherwise) work reliably is an issue that only you can test and you can do that testing with relatively little up-front investment.
If you can address these issues, you (or a qualified contractor of your choosing) should be able to pull it off.
Thanks! That was a great help. After doing a little searching I see what you mean by "no afordable way to modulate an HD signal over coax". Maybe two closets are in order to maintain shorter cable runs (1 upstairs and 1 downstairs). I guess I figured this was a more readily available solution by now...