i've also been having small problems, but i'm only new to nvidia on linux. in particular, i have often gotten the "no screens found" errors.
i got around them eventually though, but i couldn't tell you exactly how. if you posted your "/etc/X11/xorg.conf" file, or your "/var/log/Xorg.0.log" file, it may be more help to see what the problem is.
it's possibly just the configuration of the screens you are using, but it may also be something wrong with the hardware (if the same problems are on three distros)..... is this all on the same machine?
one quick fix though regarding:
"and I get their stupid little splash screen"
if you go to the Graphics device section on /etc/X11/xorg.conf (i'm using slackware, not the other distros), you can add the line:
Option "NoLogo" "1"
to not have the splash screen on startup..... although i don't know how serious you were being about the screen being a problem.
i probably wasn't much help, but i could have more to add if i saw your xorg.conf and Xorg.0.log files from the slackware install. i understand the need to format and use something you know works though.....
i'm only new to this myself, as i mentioned, but it seems that there is always something small which can fix something large.