There are a number of PDF readers around, and as an academic who spends most of the day working with references in PDF format, I can tell you that Zathura combined with a tiling window manager and a little shell scripting (for temporary bookmarks) can do most of what you say you want.
Thanks for the reference. BTW, I've now and then sent these lists to PDF reader makers. None have ever paid any attention nor acknowledged it. So I complain here :-)
