Check your document - I suspect that Schwanzspecht is a typographical error and should read Schwarzspecht - black woodpecker.

Woodpeckers Black Woodpecker Dryocopus martius, En. Black Woodpecker, Da. Sortspætte, Du. Zwarte ...
www.birdguides.com/html/vidlib/species/Dryocopus_martius.ht...

Green Woodpecker (Picus viridus). Bird which has adapted in order to make use of tree trunks ...
www.ddgi.es/espais/ipicot.htm

Your solution for Kletterfüße sounds fine to me. See the excerpts below for some ideas. (Same goes for the tail).

Bird which has adapted in order to make use of tree trunks. Apart from a robust, pointed beak, which allows the bird to make holes in the wood of the tree, its feet have 2 toes pointing towards the front and 2 toes pointing behind in order to remain vertical whilst grasping the tree-trunk. The feathers of its tail are quite rigid, providing a support whilst it pecks at the tree. Its tongue is very long and is used for removing insects from inside their long holes in the wood. When not searching for insects, the bird's tongue is curled up in a spiral inside its head.
www.ddgi.es/espais/ipicot.htm

The woodpecker's tail is also unique. The tail is strong and stiff and is used to support the woodpecker while it is hammering. The two feet and tail form a triangular support system which the woodpecker needs while searching for food.
www.alienexplorer.com/ecology/e148.html

Able to hammer wood at a rate of more than 100 blows per minute, it is no wonder how the woodpecker got its name. When hammering, the woodpecker uses its tail as a brace, to prop and to steady its body as it delivers its jackhammer blows.
www.flex.net/~lonestar/woodpecker.htm

The Red-Headed Woodpeckers have red feathers covering their whole head from the shoulders up. The Red-Headed Woodpecker has a beak like a drill, a tongue that can scoop up food, and a tail that is used for support. Like its cousin the flicker, the Red-Headed Woodpecker gets insects by pecking them out of tree bark, but some it catches on the wing. The Red-Headed Woodpecker is the only woodpecker that can capture insects while it is flying.
Most species are small to medium-sized. The Red-Headed Woodpecker is 7-1/2 to 9-1/4 inches long. The adult has a totally red head. The back, most of the wings, and the tail are glossy black. The wings have extensive white patches which are visible when the bird is perched and in flight; underparts and rump are white. The stiff tail of the true woodpecker serves as a support.
www.eecs.tufts.edu/~cabotsch/bulloughs/vertebrates/birds/ woodpecker.html

Woodpecker, common name for any of more than 200 species of birds of the family Picidae, known for their ability to cling to the trunks of trees and dig holes in the wood with their beaks. Woodpeckers have a sharp, straight, chisel-shaped bill and a long, extensile tongue with a hard, spear-shaped tip. The toes are usually in pairs, two before and two behind, and have sharp, strong claws. In a few species, one of the two rear toes has been lost. Except in the subfamilies Picumninae, the piculets, and Jynginae, the wrynecks, the tail is stiffened, with the shafts of the feathers terminating in hard spines, which the birds press against a vertical surface to help support their weight.
www.cnet.windsor.ns.ca/Environment/Advocates/Anim/pwpecker....

And finally, this reference might also come in handy:
www.animalpicturesarchive.com/animal/EngNames/green_woodpec...


HTH!