Thanks, Woofie! Great find. Stacy's grandfather-in-law scooped the seeds!
>> But it makes me think the word "hybrid" was possibly misused
My interpretation was that the seeds he was scooping came from the F1 fruits, growing on a P1 plant.
I think like so:
The pollen parent A fertilized a flower on the ovule parent B.
Both of these were "P1", parental strains, OP, and could be propagated by just saving seeds.
Next the ovule in that flower developed into a watermelon.
(Would that melon look like Parent B or like the 50-pound Schochler giant? I don't know.)
The seeds inside that watermelon are "F1": 50% genes from pollen A, and 50% genes from ovule B. Even though the plant is a P1 plant.
Next, Virgil scooped out the F1 seeds and Joe Palmer Schochler sold them all over the South, including to the Robert Buist Company, a seed distributor.
Then the F1 seeds were grown into huge braggin' melons by lots of happy people.
However, sadly for us, the seeds inside those big braggin' melons were the product of two F1 plants, not an A plant and a B plant. Hence they were "F2 hybrid" seeds, and probably had a random mix of A characteristics, B characteristics, Schochler characteristics, random intermediate traits and a few odd recombined traits.
BUT some lucky F1 hybrid varieties make F2 generations that are pretty close to the desired plants. You never know until you try. Like, some hybrid petunias "come pretty true" even if the F1 plants just pollinate each other promiscuously. But the seed vendors print "F1 Hybrid" in large letters and don't mention that you'll hardly tell the difference in the F2 generation.
If the F2 generation comes out "mostly pretty close" to the original 'Schochler', you might be able to get it "pretty stable" in fewer than five generations. And you could eat a lot of watermelon in the meanwhile!