Next step: I upgraded the Mac OS to High Sierra. The upgrade went fine, although I had to unplug my external monitor from my MacBook to let the upgrade go through.
After the upgrade was completed, Fusion would not boot the Bootcamp partition, claiming it could not find a disk to boot from. I found my problem described here and followed the well written instructions to fix this issue:
I have been running this now for a couple of days and it seems to be working fine, although definitely slower than booting Windows from Bootcamp.