I considered staying in G-P but didn't want to be changing hotels
nightly. And I'd still have to get to Fussen at some point.
Rick Steves suggests the travel base of Reutte, just across the border in Austria, a town which splits the difference between G-P and Füssen. It's a quick and direct bus ride from there to Füssen.
Reutte Bahnhof > Füssen Bahnhof = 26 min. on Bus 100 (8:05 - 8:31, for example.)
https://www.lechweg.com/fileadmin/____user_upload/service/busverbindungen/Linie_100.pdf
Staying there would also mean a direct train ride to G-P.
Reutte Bahnhof > G-P = 56 min. by train (9:01 - 9:57, for example. See DB.)
If the Zugspitze is your goal, you don't have to travel all the way to G-P. That same train line from Reutte will drop you off at Ehrwald Bahnhof after 29 minutes (9:01 - 9:30, for example. See DB.)
The Tiroler Zugspitzbahn ascends the Zugspitze from "Zugspitzbahn Talstation" (the base station) which lies a few minutes outside Ehrwald. You can see this lift (in red) on the map below - look to the left of Ehrwald:
https://zugspitzarena.com/Orte/image-thumb__72751__thumb-slider-main-lg/sommerkarte.jpg
You can walk there in 40 minutes... or you can take advantage of the bus connection...
Local buses take 6-12 minutes to get you from Ehrwald Bahnhof to the base station and run around the clock (9:34 - 9:45 for example.) See schematic for local buses:
https://www.zugspitze.at/typo3temp/assets/_processed_/c/f/csm_tza_fahrplan.jpg_97c72291d7.webp
So if Reutte were your base town, you'd be ready to ascend the Zugspitze in just 44 minutes.