I started the watermelon you know about at various times in May. If you are going to plant only once, I would say try it about 45-60 days before your hottest weather of the year. You are right that you could start a little earlier. Try to buy 90 day or less varieties. The world record type take 120 days though.
Edit: The link didn’t work quite right. If you want to see the calendar you can select it from the list of menus to right of linked page.