I’d invest in a used x86 SFF PC over a RPI for performance, you will pick one up cheap and it’ll be way better suited for a media server over a RPI.
Look into Tailscale for remote access. Very easy to setup and their free tier is generous. (100 devices I believe).
This honestly doesn’t seem that bad at all, you can change at Clapham junction and get a train to Victoria very easily. Also Vauxhall is only closed for a couple of days which has underground and bus stations. Good to know about these things but the engineering works won’t stop people getting in/out of London.