We'll be exploring Germany in late August/early September by car and, once we've explored the Black Forest and the area around Freidburg, we'd like to see some of Switzerland as we make our way to Salzburg. We'd appreciate your thoughts on a route taking maybe two days? Should we plan to overnight in Fussen or do you have other favorite spots we should think about?

The most direct route takes you along the side of the Bodensee [aka Lake Constance] which even 40 years later I remember being lovely, especially the sub tropical gardens on the island of Mainau. I would definitely plan to spend at least one night in that area so that you can visit the gardens at leisure. Another night in the Fuessen/Garmisch area would also be great I think. So much nicer than rushing through.

Start with Bodensee and drive the Aplenstrasse? Though that needs more than your two days to do it justice it can be done.
https://www.deutsche-alpenstrasse.de/en/alpine-road

Whichever route you choose will be a lot of driving for two days.

If you go through Switzerland you will need a toll vignet, as of course you do for Austria.