John, I'm with Dave on this idea, really have not seen anything to support the notion. But was curious and Googled "biodynamic planting calendar". Got a few hits, but they all seem to be sites that are selling something, whether it's a calendar or their services.
You could try just planting your watermelon seeds maybe once a week over a period of a few weeks, note the moon phase when you plant on a tag, and see which seedlings sprout fastest, or do the best. Then you would have your own data for your area to refer to next year.
It wouldn't be that bad an idea to have a succession of plantings anyway, since your season is so long. You would harvest watermelons at intervals instead of many melons all in the same week.