Why not trawl the suppliers and get samples of all the ones you like and create a unique floor, little by little? Include LPs in some spaces by all means...encapsulating resin heats up on curing though, so watch out for warped vinyl!

The Amtico ones can be cut into all sorts of shapes too, and some interesting effects can be realised. Put them in the oven to warm and cut curves with ease. Best to roll them with a very heavy steel roller after fixing for the best work. In the 80s someone I worked with drew plank lines on chipboard with brown/grey magic markers...looked ok once sealed.
Leave whatever you're going to lay (roll vinyl I am ultimately guessing) in the room for a day or so before laying it. A newspaper template of all the cuts might help too. Tape it all together and trace around the shape with a water-based pen, cut and fit. Pros seem to be able to do it 'in-situ' - maybe you could?