You only need one RG-6 cable from the dish if you have a DPP switch in the LNB or after it. If you are using a DP-33 or the like, THEY should have changed the built-in switch or sprung for a DPP-44 switch.
While 15 foot may not be impossible, the loss of high frequencies for a tuner is appreciable. If it were OTA (<900 MHz) I'd go for it. What was the component cable doing and can't you route an RG-6 cable alongside it. So if you were using an RG-6 for OTA, it should be simple to switch to Dish signal on that one. Then you could use whatever works on the OTA including twin lead and a bal-un or approximately 75-ohm, even 50-ohm cable. Or use diplexors to send OTA and satellite thru 1 RG-6 cable. Try to have as few mis-matches as possible. A diplexor is a minimal mismatch if correctly done but must have a DC pass to power the dish or switch from the receiver or power supply.
The critical one is the Dish signal to 2GHz on DP (two cables) or 3GHz on DPP (one cable and a separator).
The installers will insist on "blue" core feed-thru or couplings for the Dish signal, white core can mis-match.
-Ken