There really is no solution that doesn't involve using one of the bigger rooms, even if temporarily, or having some discreet attachments on the wall.
Unless you're running a AirBnB the spare rooms could be utilized, at least for a short while.
You could use the top of a double bed to lay things on and get some idea - perhaps standing carefully on a stepstool to get a bit of perspective. This is what I do as I don't have a spare wall.
You could use lightweight plastic hooks on a wall, with those pull-off sticky pads, and hang a white shower curtain that you could pin onto, and then fold the whole thing away?
Your need for extreme neatness seems to be a barrier for you - but folks without that hang-up, and who live in spaces much smaller than yours don't understand. You're making it difficult for yourself, because of your particular needs, and then expect folks to understand - I don't think anyone means to be flippant or unkind, they just can't see the hang-up?
Take care, find a solution that works for you
Leila