This looks/sounds just fabulous. If I was in London I'd be there immediately!
There's nothing much like that around where I live that I'm aware of. I do occassionally sing with a group that works on a wide variety of folk musics with dense harmony (emphasis on Georgian, Sicilian, and some southern African songs), but it's not a public performance.
I am studying/learning the Agnus Dei II from Josquin's "Missa de beata Virgine," and it has been deeply revealing. I think I can relate to your feeling about being inside the music, but I have far less experience than you do, so can only base that on this piece. It's challenging on many levels, not least of which is the un-standard nature of the composition related to modern, standardized, post-Bach/Baroque music.
Your liturgical footnotes sound about right to me, but I'm not expert. I've tended to listen a little more to continental renaissance/medieval music than Anglican, but I'm actively working on paying more attention to the English music. There've been a couple notable new recordings in the last few months I need to get on.