[Sephiroth]

If you have a strong downstream power level (say 5 dBmv), then installing a professionally made length of coax cable to make a single run, will not attenuate the signal to below optimum value. If you add a length of cable via a splitter or connector, then there's c. 3 dB further signal strength loss.

You also have to watch upstream power although if that's around 40 dBmv then adding cable/ 1 x splitter isn't going to push that up over limits.

My solution would be different, but may not appeal to you because thereis cost involved. I have the SH installed at the point of entry to the house. The SH is in Modem Mode. The output of the SH goes to a Powerline adaptor in a mains socket (made by Devolo - 200AV model). In another room, I have the router and another Devolo Powerline adaptor. I connect from there by ethernet to the wireless router. There is no loss of any sort due to this arrangement.

Hope that helps.