The Upload thingie is solved.. kinda. I wrote some test with LWP::UA. Uploading went super! I tried some alternative ways of parsing the form data. I called subroutines that are normally called automagically anyway. When I tried manually, it would still b0rk after 1-10 uploads (depending on the mood swing of my apache installation apparently). Anyway, I finally tried on a spankin' new Sarge with Apache and mod_perl out of the box and it worked fine there (or at least, it worked for the first 20 uploads. I didn't bother testing more).
Note added to FAQ. Move on! Nothing to see here!