OP You've gotten a lot of good input on various options. From your posts just run a new coax from the dish to the receiver, then use a RF modulator and AB switch with additional coax jumpers and AV cables. Use barrel connectors for male to male coax connections like in the storage area. NOTE: There is no reason to run the receiver input coax to the rear DS, just run it to any convenient outside access.
BTW I have a RF module at home and coax for the kitchen TV, about $10. You'll need AC power or perhaps some will work on 12V DC.