About the best I’ve done with vertical squash so far is Tromboncino. In 2017 I grew some on a jute net stretched along a bamboo pole supported on each side with bamboo teepees.
I trained the vines up teepee legs and across the net, weaving new growth in and out of the openings and along the top pole.
I also grew one up a bamboo pole by my espalier apples
I can’t grow maxima or pepo because they get destroyed by squash vine borer before making any useful product. So I’ve been running through various types of moschata to find something I like. These Tromboncino were really fun to grow - highly vigorous and they grew some awesome squashes. Unfortunately they had no flavor at all! I don’t know if it was my soil or what but they did eventually all end up in the compost.
I’m trying again this year with some other varieties grown on some new trellises I’ve been working on.