Update on Turkish Airlines voucher upgrade availability search.
Good news: seats.aero has a fare class availability search which allows me to look for upgrade inventory which comes out of J class.
Bad news: apparently, that is not sufficient. TK uses J class for both promo business fares and voucher upgrades, and apparently there is a separate (sub)class of J for how many of those J tickets are available for upgrades. That information does not appear to be available on any GDS. TK has their own GDS called Troya (who knows why). There's an API for Troya that's available at developer.turkishairlines.com but that API is bare bones and rather useless.
Back to square one :-(