Pocketbook readers can browse folders for files, have Adobe viewers and a lot of other formats supported.
Kobo apparently
maintains a database which could get messed up. Still, that thread is about fixing it, so that's not irreparable.
That's better than the Sony readers, which require special software to even see books. It appears this can be worked around with
third party software.
I haven't had the chance to test any of them thoroughly, and don't know the pricing where you are, but I hope you'll find something useful!