To elaborate...
OP can send either 720p or 1080i (both HD) over RGB and Dolby Digital 5.1 PCM over either or both of the LR. No need for any sort of converter at either end.
Unless the destination tv is HUGE or OP sits closer than arms length to it, the difference between 1080i and 1080p will never be detectable. If source signal is satellite or cable, it's 1080i anyway. Very little 1080p is broadcast because very little 1080p TV content is recorded.
For movies, get a Roku or Chromecast plug it in behind the TV, no cable fishing needed.