I almost always agree with @rayrose and this is another case where I do. First, in spite of lots of people saying the thin their melons, I never have and find no reason whatsoever to control the number of melons per plant- they will support whatever they retain, and if they set to many some will be aborted as Ray said. It can happen even after it sets fruit and the small melons start growing. If there are too many, the plant will just stop feeding some and they will turn black and fall off if there are too many. If not, they will grow to maturity. I’ve seen plants with only 1-2 melons and plants with 6-8 melons both produce similar sized fruit. The number per vine doesn’t seem to matter.
I fear you are in an uphill battle trying to grow watermelons on a trellis but I completely understand your reasons for doing so. I my experience, for whatever reason, while the vines will certainly climb up a trellis, the higher the vine gets the harder the plant has getting proper nutrients to the developing melon, and the result is that melons more than a foot or two above ground level just don’t do well at all. Not only do they not get large, but they don’t ripen well if at all. They sort of get to the size of a softball or a little larger and just stop and stay there all season.
Of course you have already started your project (I hope) and I’d never want you to give up based on my experience- and honestly I haven’t tried very much with trellises. You also may have better soil or climate or a different type melon or some other reason that it works for you, so I hope you prove Ray and me wrong! Please keep us posted, and good luck.