You can't do this with the HDS-600RS out of the box as it has no modulator. You would need to add a modulator and drive it from one of the SCART outputs, and for remote control you would need a separate device like a Powermid or something. It can be done and it will work but not sure how expensive it will be. Modulators used to be a couple of quid as a component (and can be salvaged from old VCRs). They can be directly driven by the SCART outputs, and just need a power supply. But now they have become a consumer item put in a nice box they can be £20-£40. Powemids are about £25 a pair. For my money I might be tempted to put that towards another HDS-600RS (especially seeing as Amazon have them at £179!).
One other solution might be to fit a quad LNB, keep the Sky+ box cabled up and use it in the other rooms as you currently do, then use the HDS-600RS as your main box.