Faced with a similar situation a while ago, I chose to install Slackware Linux. It's still possible to install the base and network sets (A and N for old Slackware users) via floppy.

Another helpful tool for Linux users: the old parallel-port Zip drives. The driver is a horrible kludge (and I don't think it's available for NetBSD), but with it, you only need to install enough via floppy to get the Zip drive working.