I would say Fussen, because it is bigger than Schliersee. Also, I note that it is near Garmish P-K, scene of the winter olympics in the 30s. There is a stone stadium, which resembles a fortress and shows delusions of grandeur (and is a tiny bit like the old wembley stadium, clearly the style was popular). It is ringed by mountains, and you can imagine the nazi leadership watching the sports there. Fascinating comparison with the olympic stadium in Munich, that was built only about 40 years later, but a whole different era.
Also some great scenery (waterfall) at GaP, it is near Germany's highest mountain.
King Ludwigs famous chocolate box schloss is somewhere down in that direction as well.
The holidays in germany are staggered, so each Bundesland breaks up on a different date. Summer hols in Bayern are from beginning August to mid September, so I guess the holiday cottages are filling up with people from outside.
Half term here will be approx 6 weeks before the beginning of August, but again, it will be different weeks for different Bundeslände.
Are all these really full???
www.urlaub-badfeilnbach.de/ferienwohnungen.htm
this site shows availability ("Verfügbarkeit") for each holiday house - Ive done a search for Oberaudorf, which is a very beautiful skiing village with a summer slide, cable car, walks, bathing lakes within walking and cycling distance. But there are lots of places.
www.fewo-direkt.de/oberaudorf/s/865/fa/find.squery