I actually made a similar arch this year. However it sounds like you didn't give them anything at all to grab on to. You need to put some sort of netting over the arch so they can grab onto something. The tendrils grab onto small things and cannot attach themselves to inch thick pieces of wood or smooth PVP pipes. How wide is this structure? The one I made has the two PVC pipes 4 feet apart. I wouldn't trust the twine with the kabocha squash myself. You can try just wrapping that twine all over the structure like between the slats and all so that you give them something to grab on to.

Agreed.

The tendrils on vine crops need the right things to grab -- twine, wire, netting, thin bamboo poles, slim branches, etc.

Anything over an 3/4"-1" is unlikely to work at all.

OK, I see that the problem is the slats are too big. I'll get some of the cheapo scrap fencing we have laying around in the community garden and lay some on top of the frame. Just as a side question, if the fencing is thin metal, is there a chance it can cut through the vine when it becomes weighted down a big? It's not chicken wire thin, but it is thinner than concrete reinforcing mesh.

When trellising large-fruited vines people often make hammocks for the fruit by tying pantyhose, old t-shirts, or some other sort of stretchy material to the strongest part of the trellis and using that as a cradle under the fruit to take the weight off the vine.

I dont know about using metal, I would think it would get too hot in the sun and burn your plants?

Metal shouldn't be a problem. Many people (including me) use CRW or Cattle panels as trellising with great success.