RE DNA analysis: this is exactly the type of algorithm I have some expertise in, and was imagining in my speculative fancy; it is true that one needs a substantial data set to get any traction. But large data sets may be available. And the fewer constraints imposed on the tune (e.g., if you don't demand a tempered scale or a strict time signature), the more data you'll need to adequately sample the larger space of possibilities.

There are large data sets - look at the ABC corpus (you could easily harvest all of it). But there aren't large datasets of usable quality for this kind of music. ABC versions of tunes have been coded to wildly varying standards, and no algorithmic comparison could make sense of them all. You would have to edit your own and proofread every bar.

the fewer constraints imposed on the tune (e.g., if you don't demand a tempered scale or a strict time signature), the more data you'll need to adequately sample the larger space of possibilities

ABC (like most other computer coding systems) says nothing about microtonal variations in the scale. I doubt time signature would be much of a problem (see the examples I gave just above, where a tune has a clear identity despite having variants in slow 3/4, medium-pace duple time and fast duple time). But trying to be over-consistent about it may be a problem - the transcriptions on TheSession.org (one of the largest ABC corpora) will be useless, because the site admin enforces loopy restrictions on the metres you can submit, and you can't tell when that policy has corrupted something.

Schenkerian analysis is a black hole of complexity quite irrelevant to this sort of investigation.