Note that the design is very similar to -- but much simpler than -- D779n13: the first strain is a straightforward 8-bar period (though Caplin would call it a hybrid theme because the pedal point tonic precludes cadential definition); the second strain consists of a contrasting middle that is a slight variation of the first strain transposed to III, and a literal and complete reprise of the first strain. All of these are elements that are present in D779n13, too, but in distorted form.
The resemblances are strengthened by the fact that the two dances come from the same time period: D 779 was published in 1825, and three German dances of D971 appeared as Schubert's contribution to a Carneval collection in early 1823.
Ternary form designs with the contrasting-middle-as-transposition may be found throughout Schubert's dances, though by no means in large numbers. In D365, only n32 is a ternary design and it follows the model of D971n2 (see graphic below). In the waltzes of D145, n7 fits the model (Eb-c-Eb); in the ländler, n2 (Eb-Bb-Eb). And so on.
It's very easy to imagine these designs originating in improvisation: one uses the same musical material and maintains the phrase design for the dancers while introducing a note of variety and extending the basic 16-bar form from 32 measures (with repeats) to 48. At the same time, for Schubert, the blocking out of key areas by 8-bar thematic units would give an opportunity to "absorb" the sound of a particular modulatory pairing, both going and coming, so to speak.