I've dreamt of vertical, but it does sound like a bit of work.
I saw a watermelon vine growing up into a small citrus tree in the garden of a pensión I was staying at in Cunén, a small village in an enclosed valley in the northern mountains of Guatemala.
The owner of the pensión explained to me that the garden had been his wife's purview but that she had passed away in an earthquake the previous year, so the garden had been left untended after that.
I was startled to see half a dozen half-grown watermelons hanging from the citrus tree in the garden there.
It then dawned on me that that was the method watermelons developed to distribute their seeds, since when the fruits ripened and fell they would break open and animals would come eat the pulp and seeds, later distributing the seeds in their droppings.
So mbmango and Simon, if you maybe have a chainlink (or other sturdy) fence, why not let your watermelon vine run up and along the fence. The vine will hold onto the fence with its tendrils. And allowing the vine to grow above the ground may likely minimize infection by powdery mildew.
Just my two cents' worth . . . .
Paul M.
==