My RV has a centralized control box for the source of input to all TV's. You have to change the source of the signal on the control box when you switch between sources of signal (ie: TV, Cable, Satellite) The satellite connection to the centralized control box is a female coax cable. The Dish VIP 211Z receiver does not have a coax output source, but I does have an HDMI output. Can I use an HDMI splitter to connect to the centralized control box by running an HDMI cable from the Dish receiver to the HDMI input source on the splitter and then running a coax cable from the coax output source on the splitter to the female coax connection to the RV's centralized control box?