I Have Leeks!
The second year the leeks didn't get big enough either, but one of them did bloom. Again, I left them over the winter. And again they did just fine.
This year I found new leek seedlings from the seeds that blooming leek produced. Back in September I reported that the leeks had yet again failed to produce stalks big enough to use, so imagine my surprise when I pulled one that had seeded in an inconvenient place as I was cleaning the beds for winter and found that it was indeed big enough to use! In fact I found enough that were big enough that I could make my yummy leek and potato soup!
So it only took three years. I'm patient, because it's no work at all just waiting. I had 5 blooms this year, which means even more leeklings next year. I will just keep letting them do all the work and enjoying the results :)