Ok, I'm making the assumption that the Coax run from the satreceiver to the dish is a dedicated run, outside of the coax loop running to the rest of the rooms. I guess I see a couple of things you could maybe do, but let me preface this with the statement that I'm an intermediate beginner at best.
1.) Move the receiver to the great room. Run yourself a new coax wire from your dish, through the attic, and into the great room. It would be your choice whether you try to mount a jack in the wall and go fishing or simply run the wire down through the sheetrock and down the wall inside paintable, plastic conduit. I've done the latter several times with speaker cable. So then you could attach your bigscreen to the Sat Receiver via S-vid or better. Then make the coax connection to the wall jack that feeds down the wall into the TV on the main floor.
2.) Attempt to hijak (splice) your dish coax wire into the existing coax wiring loop. Did you have CATV before? If so, just find the entry point for that prior coax connection into your home from the cable company, do a little cable cutting and splicing, and run that into your dish. That's the way the DirecTV boys do it when they're being lazy. At that point, all coax jacks in the house should be receiving the satellite signal...I think...
3.) Do nothing except buy the big screen and plug it in to what you already have. Your obviously going to be much better off than you are today. Probably 90% of households in the US connect their satellites their TV's in this manner. Will it give you best audio and best sound? No. But do you have high end Denon 7.1 equipment and all high end monster audio fiber optic cable and super speakers? I'm guessing no (but it would be cool if you did). So who cares? Do it a step at a time. You can purchase the big screen today and be ready to watch the Series and be good to go. You can later start changing your wiring around to make it better if you so desire.
Of course, this is all coming from a cheap-arse!
