A Hubbard or Banana squash on a trellis... I don't think so. Those things are born to run along the ground, aventicious roots and all. Yes, I know they will climb up your tomato cages and such... so... yeah... you can do it. If you find a way to support those large squashes, which will otherwise tear the whole vine down with it.
I say you should plant them next to your side yard, guide the vines onto the grass and such. I agree, it does look like heck. Par for the course. Works great.

Oh well, I was afraid of that! I live in a residential neighborhood, the neighbors already put up with a lot from me, lawn-care-wise. Last year when I planted them in the ground, each of the 4 or 5 plants I had going sent off 2-3 long vines, each in a different direction. They were impossible to mow around, but not dense enough to suppress (or camoflage) the grass. Clearly I just have to plant more next time. ;)

Maybe next season you will get enough squash that you can share with the neighbors...that might help them except your grassy yard LOL!

Oops...that should have said accept your grassy yard LOL....
it's too cold for me to think correctly LOL!

LOL sunny-- I think many of them already take exception to my grassy yard!

Scored three gigantic (5.5ft x 4ft) pieces of clean cardboard out of a dumpster today, which will become the foundations for my new beds-- there's no turning back now!

a winter squash/pumpkin vine grew up a dead apricot tree in our frontyard this year. the various growth stages of the vine were beautiful throughout the summer,especially the 5 ripening pumpkins. but today the vine is limp and soft from last night's freeze. i wonder if i should harvest the pumpkins, even though some say to keep them on the vines until the vines die and turn brown. ?
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Here is a link that might be useful: {{gwi:868330}}

They will need to cure for a bit before you cut into them and the sun will help with this. They don't need to be on the vine to cure. You can also cure them at room temp in a place with good air circulation inside or on a porch, etc.

I have read that you can grow the big squash on a trellis if you use something like old pantyhose to make a sling for them, to hold their weight. Attach the sling to the trellis. It would have to be a very strong trellis, however, to hold all that weight.

I put cardboard around my squash vines this year. It kept the grass and weeds down very well. You could cover this with mulch or even grass clippings if you wanted it to look nice.

Here is a link that might be useful: My country blog

I once had a large squash vine volunteer in the garden. We let it wander to see what it would be. Ten feet from the garden, across the lawn, it found an oak tree and 20 feet up the trunk, it held its own -- no pantyhose slings, no nylon ties -- even with four large squashes that made jars and jars of wonderful food for the babies and us!

For general trellising, I have made portable frames of 4'x4' lath to which is stapled coated chicken wire. I attach the frames to 6' metal fence posts and train cucumbers and squash vines up and over. I've also used them for tomatoes anchoring those plants to the chicken wire with garden twisties. Everything is removeable, reuseable and portable to allow for fall clean-up and crop rotation. But because I love garden experiments, I am experimenting with bambo tripods this year over some of the cucurbits. Garden twine is wrapped around the tepees and the vines trained to trail back and forth through the twine. Winter squash vines are so long that they are allowed to go from one trellis to the next! A veritable jungle of vines by the end of summer! Good luck and garden blessings.