Yo Dawg,
Consider fishing that from the speaker hole, over and into the bedroom closet.
When the dish installer installed mine, we needed to get a 5 wire cable (stereo audio and componenet video) from the bedroom closet where my receiver and sat controller is, over to the bedroom TV above the window on the door side.
Used a fish tape from the TV antenna jack/power supply wall plate, up into the ceiling and over to the speaker, then over to the ceiling mounted TV jack above the TV.
Not sure what you are running or where you are running it to. Perhaps you are extending the roof coax and running it to the UDC? If you can get the wire over to the W/D prep, you may be able to follow the plumbing to the utility area and over to the UDC.
That's how we got an HDMI cable from the bedroom receiver in the closet to a wall plate in the storage area of the basement.
Have fun, take your time, use the existing ceiling items as access holes, use a fish tape - it will work out.
Moving this thread to Landmark Satellite Television forum.
Jim