I remember The Amateur being amusing; I like Hartley in general BUT I love Trust. Definitely recommend it, sort of his hallmark film. Really sad about Adrienne Shelly and the whole fake-suicide murder thing...
I'm with you on the Lynch, not so much the Tarkovsky. Regarding Paris, Texas - I agree, really an amazing experience, BUT, a warning: you need to watch it uninterrupted, with zero distractions, and your full focus. Otherwise it's completely ruined, in my opinion.
Actually, these are all a little artsy-fartsy, but the requirement was obscure, not necessarily non-mainstream. Allow me to recommend then one of my very favorite films and Albert Brooks' magnum opus, the highly underrated Defending Your Life. I do so love it.