Later I realized I could have done the job, and faster, using just two disks: one in the computer writing the disk images and one in laptop reading the disk (and then swap disks & overwrite with the next image). D'oh!
https://www.youtube.com/watch?v=p5o6NQmEA-8
(Yes, this was a real, official thing that was available from Microsoft)
I was then setting up my own little TCP/IP network with a NFS server on my two machines, connected via coax Ethernet using NE2000 network cards.
Thank goodness for CD-ROMs. Only a few years after that, I was able to just go into a computer store and just buy a single CD with Yggdrasil (or RH or Slackware) which made the whole process much easier. As long as your system could boot off of CD-ROM... sometimes you still needed to make a boot disk.