In my square foot garden, I have a trellis beside one edge. Am I being too ambitious to try to put a square for pumpkins, then an empty square, then a square for watermelon along the edge?
Melons and squash are vigorous growers. You are trying to use your vertical space and try to try to trellis them upwards. Yes, this is ambitious. ;) It's a little bit harder than it sounds, since they have a little bit of a mind of their own about where they want to grow. If you are gentle and patient, you should be able to coax them into growing up the trellis and then gently bind them to the trellis. Even with this approach, their leaves will probably spread out so much that they'll take at least two square feet.
It would be better if you gave them two square feet from each other, but with only a single empty square they'll just compete with each other for sunlight in the middle. Try to spread them a bit further apart on the trellis and make sure they aren't shading out the plants in front of them too badly.
Some other options that would work in your square foot garden:
Don't underestimate how much watermelons and the like spread. I've tried growing small pumpkins and mini watermelons before, and they can vine out easily many feet. I've never tried growing them up anything like a trellis, but my sense is that even small pumpkins might be too heavy for much upward growth without potential breakage of the vines. I had a wire fence around the edge of my garden, and I don't remember them growing very far up it, so I would expect them to grow more outward than upward.
In short, give them a wide berth (honestly, probably at least 2-3 empty squares between them) or be prepared to chop away at them to keep them from tangling up with each other and overtaking any other plants.