Small mesh wire cages are it, really.
Although, don't see why you can't do trellis. It is how I solved my exact dilemma. An outdoor cat helps.
I don't do cats viking. Every human being who is like a cat is either in jail, an asylum for the criminally insane, or is otherwise working on wall street.
Any chance you could post some pics of your trellis? How do you manage to have them bear weight without snapping off the vine while elevated?
Well, first step is growing smaller, sweeter varieties that won't snap. lol.
Ok, well, that isn't the best of advice, but helpful.
The vine will, in most cases, thicken enough to hold its fruit without breaking as long as you prune the new growth after fruit set. I'm using 6' vertical trellis (nothing overhanging like the pros), and it works fine--but I dont let any one vine make more than 3 fruit except my cucumbers.
On my heavier pumpkins and watermelons, I simply place burlap folded under the bottom and wrap 4 ropes and tie to the trellis to support the weight. The wooden cedar trellises I use are strong. They are $20 each at Home Depot. I tapped them straight into the middle of my raised garden beds, and they are only supported by crossing bamboo or small wooden stakes.
I can take a picture of the setup, but it won't do much justice yet since the melons are only just germinating.
Remember, pruning is key. Remove all growth within 18" of the base and prune new growth after 1-3 fruit are set per vine. Fewer fruit than growing on the ground or in sky trellis, but the difference is you can grow more plants in a compact manner to make up for it.
I use to grow them off mounds in open fields and it took up a lot of space. A lot would produce, but vines and fruit would die often to the moth and animals.
Raised on a vertical trellis, success is virtually controlled. Mine are only spaced 18" apart, and I stagger the melons in a zigzag pattern. I've discovered higher pollination success when flowers are off the ground.
