I've never thinned a watermelon vine, and it doesn't make sense to me to do so. You need as much foliage as possible to develop the sugars for the melons. I've always let them sprawl, never tried a trellis. The vine tends to abort any melons that will overload the vine, so even thinning the fruit is questionable. I say let it go and let it grow.

Alright then, thanks. I think I'll give it a shot.

Watermelons need a lot of room to do well. The idea of pruning the vines probably comes from folks trying to grow them in too small of a space. I've taken the growing vines and directed them around in a bit of a circle around the plant to minimize the sprawl.