I would skip using Unifi and look at Cambium as these are a far better AP for density and coverage.
Cambium Networks XV2-2X00A00-EU - Cambium Networks XV2-2 1774.5 Mbit/s (lambda-tek.com)
You may want to contact our installers below who can provide hardware and install costs for Cat6A cabling, they also just offer supply of AP's at a much cheaper rate then the website above suggests.
WiFi - WM Networks | End to End IT For Businesses