It took a bit longer than advertised, but the Spathiphyllum seeds have germinated.
There are a lot more than I initially expected to have; it turned out that even though only one of the bumpy things on the spadix definitely changed color, several of them, including the green ones, had been successfully pollinated. So a few days after I started the first batch of seeds, when I went to remove the flower from the plant, the spadix sort of exploded into more seeds. Since I am helpless to resist seeds, I went ahead and picked them all out and sowed them on vermiculite in the basement with the first batch.
I got 75% germination from the first batch (6 out of 8); I don't know about the others, because I didn't count the number I started with. Germination took about 11-18 days, only slightly longer than the 10 days predicted on-line.
The question of whether or not it is possible to grow peace lilies from seed, which once seemed plenty urgent, has now more or less been answered. (True, we'll still have to wait until they survive transplantation and get big enough to bloom and everything, but it seems like the biggest obstacles -- pollination and germination -- are out of the way.) We can now move on to why one would do this. Anybody? Theories?