I know others are totally successful with transplanting, but I've always had better luck direct seeding melon and squash type plants. Transplanted ones sem to be stunted compared to direct seeded ones. I haven't tried it in a long time, the ones I tried were volunteers in the wrong place so they may have been disturbed more than the purposely started ones, and you have had good success transplanting them, so don't let my experience stop you. Your technique may be different from mine.
From what I saw on Mapquest, you are a bit more in the lowlands than the mountains and hills I grew up in, so you should have a great climate for growing watermelon, lots of long hot days, whether you direct seed or start them indoors to get an early start on the season. Even at higher elevations and roughly the same latitude in Tennessee we had plenty of time for watermelon. I don't know how much room you have or how many you intend to grow, but why not try it both ways and compare the results. Your direct experience is going to be a lot more valuable to you than my opinion.
Do you remember the variety of watermelon you grew? If so, you might want to check to see if they are hybrids, just so you will better know what to expect. You've been around enough that you probably already though of this, but I'll mention it anyway.
Good luck.