First thoughts: Messy, buggy, wasting potential, and a sledge hammer to crack a walnut.
Sky Q already has a feature built-in to support several additional rooms. It's called Sky Multiscreen. The main Q box differers from the Sky HD box in that it supports something like 14 tuners rather than two despite the box itself still only using two feeds from the LNB. The purpose for all these tuners is so that main Q box can supply signals to small player-only boxes called Minis.
Minis have no inputs for satellite signal cable. For most people, all they'll see is a power lead and the HDMI cable going to the TV. The boxes have Wi-Fi, Ethernet and also Powerline Ethernet support. This is how each Mini receives live TV and recorded programs from the main Q box.
To all intents and purposes, a Mini acts just the way an extra Sky HD box would with a full multiroom subscription. Whatever package is on the main Q box is replicated on the Mini. It's possible to watch different channels at the same time that the main box is being used. The Mini can pause and rewind live TV. It can be used to set its own recordings without clashing with the main box or other Minis, and to play those recordings regardless of what the main box or another Mini is doing.
Sky's multiscreen package costs £13 per month on top of the main box subscription price, and there's a one-off fee of £75 per Mini. Having Multiscreen also unlocks Sky Q's Ultra HD signal for the main box.
Changing to Sky Q and then adding the sort of HDMI-over-Cat-cable distribution system you're thinking about is a bit pointless. You might as well stick with the HD box because you're not gaining that much by swapping to Sky Q. Sure, you get to record more channels at the same time, but the box itself can only show one channel or play one recording at any one time, so all the extra rooms only see the window on what is being viewed in the main lounge. For that, you might as well stick with Sky HD.
Where your friend/relative/customer is happy with the idea of sharing one box to three rooms, but wants better picture quality and to retain compatibility with Sky Eyes for control, then there's a smarter way and, better still, it makes use of the existing coax cable.
There are boxes called modulators which will turn a Sky HD signal via HDMI in to the equivalent of another Freeview HD channel. That means a vastly improved signal over the existing coax that your friend is currently getting with Sky's analogue RF2 signal. Have a look at the Edision HDMI Modulators. There are a couple of versions. The one I would recommend has an orange frame around the LCD display window, and it has two connections for RF signal pass through. This last part is important because it means that the box integrates with the home's existing Freeview service and allows the Sky Eye signal to get back to the HD box. That means the TVs retain access to Freeview as an alternative to watching the Sky signal.
The TVs that are going to be used with the Edision or similar boxes need to be able to decode MPEG4. Most recent TVs with a Freeview HD tuner seen to fit the bill, but it's always worth checking just to be on the safe side.
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