the schnauzers,
You are quite right, so I have summarized the most relevant train trips from Fussen to both Frankfurt Airport and to Munich Airport. To Frankfurt is complicated, as there are 2 to 4 separate trains involved. I am not going into the details of that (those that want or need it can find them on German Rail), but here are the relevant trips:
601a - 702a 717a - 840a 851a - 1101a
706a - 857a 936a - 1206p
806a - 914a 938a - 945a 1003a - 106p
905a - 1057a 1103a - 123p 135p 206p
1006a - 1052a 1115a - 1135a 1203p - 306p
To Munich the situation is a bit better, but even there 3 legs (including one for 2 minutes) are required for the 3 hour trip (not 2 hours as previously assumed for driving):
601a - 708a 715a - 808a 819a - 821a 831a- 906a
702a - 857a 905p 955p
806a - 1005a walk 10 minutes to S-bahn 1023a - 1106
905a - 957a 1006a - 1109a
It looks to me that the rail approach will have major waiting time from pit stop release to the first train of the day. If it were a decision up to me, I would take a car despite the fact that I have rented a car once in several decades for travel within Europe, strongly preferring the train trips.