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Why not just locate the AP in BR01 rather than the loft space? It removes a layer of ceiling between it and the clients. Also if you're bothering to do this then buy actual decent AP's, not ADSL routers - a 2.4Ghz Unifi AP or AP LR kit will be inexpensive on the bay of thieves and is easily feeling mounted (LED can be turned off via the web interface). Why 2.4Ghz? Because with thicker walls 2.4Ghz achieves better penetration than 5Ghz and as you state ADSL router, you'll be WAN limited anyway even if you go VDSL.
All true, but more complicated to implement.
The OP's original plan makes good use of the 'AP' having multiple Ethernet ports to keep things simple.
With a single port AP such as the AP-LR you suggest you're going to need more wiring and probably a switch as well.