I don't believe I've ever heard of Dolls before, but I will definitely have to look into that one. I've never actually seen In The Mood for Love, but I do know of it - mainly because I found it while searching for similar films to Lost in Translation (which was directed by Coppola, who coincidentally was inspired by In The Mood for Love!). ITMFL is one that's been on my watchlist for a long time but I suppose now I'll bump it up a few places :)
Lost in Translation (also recommended if you've never seen it) very much focuses on the two main characters' emotional and intellectual connection more than anything, which is something that I was thinking of while playing through Set Yourself on Fire too - this combined with the whole peeking into the characters' private worlds like you say makes it much more intimate than it'd be otherwise. Honestly I wish more stories/media could be like that, though I suppose if everything was like that maybe it wouldn't feel as meaningful?
And yeah, I can totally understand being inspired by music more than anything else. Like, if music can evoke a certain feeling or mood or sense of place then surely it can be put into words, right? Like it's something you have to translate, but it's difficult to really capture the same idea that the music is giving off. I dunno, maybe I'm missing your point. Sometimes things make sense in my head and then once it's on paper it doesn't haha. Either way I'll have to go watch both of those movies now!