The watermelons and pumpkins won't cross, that's what everyone that I've asked says. And I'm pretty sure you can trellis watermelons just like other melons.

There are two reasons that crossing is a non-issue. The first is what phantom said: watermelon and pumpkins cannot and will not cross pollinate each other.

But, even if they could....you would not be able to see (or taste) the results of such a union until you harvested the seed from THIS crop, planted them and grew them (next year).

All of the genetic information is in the SEED. The seed you're planting this year is already 'pre-programmed' to deliver exactly the cultivar of watermelon (or whatever) you've planned on.

I posted a picture of the vertical garden I built a few years ago over a 4x4 raised bed that began as a square foot garden. The pantyhose thing works with larger melons as long as your supports are strong enough. I added 2 horizontal supports parallel and right next to each other on each side of our vertical garden so the larger fruits can balance between the pipes.

I'd love to see pictures of what you are doing.