Mine have always traveled across the ground.
The squash can get quite large they would be tooooo heavy on a trellis

That's what I assumed but wanted to check. I have about 3-4 feet around all sides of it. Do you think that'll be enough room?

Well could be, then if it very healthy maybe not. I think 3-4ft would be ok. If it gets out of hand just snip off some of the trailer ends and stop it from spreading. Don't water from above No wet leaves(fungus). Watch for squash bugs, You should be on your way to some nice butter nut.
Arizona
PS I am 1 blog below you trying to figure out what we planted -that's my shoe

This post was edited by campv on Mon, Jun 2, 14 at 17:00

Last year I let my butternut squash climb up my chain link fence. I loved it. It was very easy to pick the fruit.