Ahh, fuggit. I'm gonna go out on a limb, and suggest... Vermouth, neat. Especially if you're having the borscht as an appetizer, why not have an aperitif? Either white or red could work. There's a number of artisanal products starting to get a slightly wider distribution- Vya, Falset, Carpano's Antica Formula, or even the Chinati of Cappellano or Vergano. Eric Seed of Haus Alpenz will also soon be bringing in the last remaining independent Vermouth de Chambery, Dolin.
Some slightly more traditional, if no less random thoughts:
Champers, dahling.
Chenin- either demi still wines, or sec bubblies.
Off-dry ross of Pineau d'Aunis (though that's my answer to everything).
Lpez de Heredia- either rosado or bianco.
Something Alpine with a rounder mouthfeel and nutty notes- say Kerner or Blaterle, maybe Altesse.
The whites and ross come to mind more quickly than any reds, but here's some attempts:
Dry Lambrusco (yeah, yeah, probably cheating w/ the bubbles...)
Various lighter bodied Loires, chilled- say Ollivier's Granit Rouge.
Hmm. Trying to find some fuller bodied choices...
Riper Barbera- recent tastes of Cappellano's AB Normal and Cascina Roera's Vino da Tavola are what prompt the suggestion.
Decent Willamette Valley Pinot Noir- there's been threads here of some good ones. Thinking of the volcanic soil sulphur funk pairing with the sulphur-y earthiness in the beets. Mt. Etna esoterica like Occhipinti, Terre Nere, COS, etc. for the same reasons. (whispers:) (And Grenache.)(Maybe.)(Especially Canonau, for the same volcanic thing.)