I have the common problem of using the slingbox and having a HMDI to my TV. Can I split the coax coming into cable box and run one coax to a (coax to a HMDI converter box) and then run the HMDI output to my new 1080P TV? The new TV has a tuner. Then can I run the other coax input into the cable converter box which goes to the cable set top converter/DVR box and use the rca component outputs to the slingbox? Then can I run output from slingbox rca components to TV inputs. Can I tune the TV using its own remote and when chosen, switch the electronic setting control on the TV to watch cable set box DVR. This way I would not need to use the HDMI out put plug which disables the component outputs. I use Scientific Atlantic set top box. I understand the limitations of the set top box outputs. It is so confusing.