You can certainly grow it on trellis, as long as you have a good way of tying the fruits.
In my zone, the only way to mature a watermelon is to grow it in a cold frame that gets open just a bit during our 'hottest' summer hours (72-80F). It stays closed all the other times. I also start the seeds indoors, growing in 4" and then in gal pots then transplant in mid June (be careful, they do not like their roots disturbed). Seeds put into the soil directly will not get me a ripe watermelon here.
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