I did find the answer about cross-pollination: watermelon is insect-pollinated so a separation distance of 1/4 mile to 1/2 mile is suggested. Or bagging some female blooms and doing hand-pollination.
(I've never done hand-pollination of anything, and also my western WA summer nights range from cool to cold, so I can't volunteer to grow any out.)
Our first generation will be for-real serious preservation of an heirloom, at least until several seeds banks add it to their long-term freezers. So if anyone thinks they're likely the only ones in their neighborhood growing watermelon, volunteering would be really angelic.
I guess Vavilov doesn't freeze these, I guess that instead of freezing, they propagate it every 6 years so the seeds stay fresh but accessible, yet risk genetic drift and put a lot more labor into it.
Also apparently, 'Schochler' must be an OP strain by now. That's good news!