One caveat is that the tricky part could be avoided, it just didn't work out during the route creation. And here go some details.

Day 1: from Oberstdorf/Spielmannsau to Kemptner Hütte (~900m, ~7km)

Given that there is not that much to cover in the first day, I would highly recommend to have lunch at Spielmannsau. The food at the restaurant there is great.

Day 2: from Kemptner Hütte to Prinz-Luitpold-Haus, passing Eissee (~1350m, ~18km)

It would be one of the best days. The way doesn't seem to be popular, at least in this direction, and the views are just amazing. Keep in mind that this is quite a walk.

Day 3: from Prinz-Luitpold-Haus to Edmund-Probst-Haus, passing Nebelhorn (~1170m, ~17km)

The descend from Prinz-Luitpold-Haus is great and there is just a fantastic waterfall on the way down, but you would need not to miss it, because it's slightly off the path. After that descend, a paved road starts. I would recommend to change route from that point on. If you are fine with some scrambling, then following the signs toward Edmund-Probst-Haus from that point on could be an option. If you choose to continue with the route, then don't take the detour from the paved road. The path there seems to be unwalkable and to be populated with insects who would be more than happy to hunt you. After a few kilometres of paved road, a nicer path starts again. At some point though, it's a bit difficult to find it and it goes through grass and bushes that are full of the same hunting insects.

Day 4: from Edmund-Probst-Haus to Schwarzenberghütte (~310m, ~9km)

Passing Nebelhorn could be an option on the forth day as well. As mentioned at the very beginning, there is a road to go up and down and so you don't have to do any climbing if you don't want to. The way to Schwarzenberghütte is really nice. The hut itself is something special. It definitely has a its own character and it's worth staying there at least once. A warning would be that no one speaks English there.

Day 5: from Schwarzenberghütte to Landsberger Hütte, passing Schrecksee (~1180m, ~18km)

There is a forest road on the other side of the river and so there is no need to go along the paved road all the way. The path starts at a bus stop, where it becomes absolutely clear that following the road would be super dangerous. It could be a bit tricky to find it at first. It goes through the forest and doesn't seem to be popular. Schrechsee is one of the most beautiful mountain lakes I've ever seen. I would definitely recommend to visit it one day or another.

Day 6: from Landsberger Hütte to Gimpelhaus (~800m, ~14km)

The way is really nice. It goes through forest, but of a different type from the day before. Following the paved road after Rauth would be suicidal and so you're better find another way. Gimpelhaus is lovely and may have live music of a fairy take type.

Day 7: from Gimpelhaus to Neuschwanstein Castle/Füssen (~740m, ~20km)

That would be another nice day, while finding the path could be tricky sometimes. There is also always an option to finish somewhat earlier in Reutte if weather requires.