It will only flower and set more fruit if it is continuing to grow at a fairly strong rate. Plus to mature another melon it would need to maintain the old leaves pretty healthy or grow new ones. I've been able to fruit Star Brite from late June until fall freeze but I have to keep the plant growing and spray the leaves for foliar diseases. It's really easier to have two plantings. One as early as possible, late March here, and another in late May. Short answer: your plant is done unless you can force it to grow again. That's not easy if it has stopped.

If you are going to deadhead your zinnias for continued flowering, keep in mind you are going to have to step through the watermelon to do so. Plus the watermelon are very aggressive in their growth and it would take constant attention to ensure they don't smother the zinnias.

If you got your seeds from Burpee and sowed them and that is what produced this "odd" vine and fruit, there is no way it is the result of a cross-pollination from that season's pollens anyway. Any cross-pollination that might have transpired would not be evident until growing out the seeds from that crop of fruit. It is however possible that there was an oops in packaging and a seed was from some other variety that it wasn't labeled for OR if it is a hybrid variety the seed that produced the "odd" vine/fruit did not adhere to the expected/typical rules for F1s or their breeding program OR if a hybrid, that seed's genetics had reverted to traits of one or both parent plants different from what was expected OR if not a hybrid, Nature had simply stepped in to alter the genetics and provide a "new strain". Nature is very good about messing with us. :) But these "flukes" are often the beginning of new varieties that are much loved. It happens not only with seeds, but also one will hear of "sports" from mother-plants with variations off of the expected. The only "catch" with saving seeds from the "odd" one would be what it cross-pollinated with. If you only grew the one type of melon and no one else within a certain radius grew melons, you can feel relatively safe in knowing it crossed with just the one variety you were growing. Keep that DOCUMENTED. If others were growing melons, find out what kinds so you can keep documentation/notes of the *possible* cross(es) made with other varieties. Do grow out the seeds it produced if it was a good melon in your opinion. If you are lacking enough space to grow all of the seeds in the next season, ask other reliable gardeners to trial the seeds with you. This "testing" is common, gardeners helping each other out by growing things, documenting relevant information not just on form but also habit, flavour or scent, etc. AND saving seed while insuring it is "pure"/not crossed with other varieties. It also allows you to find out how a variety or strain does in different climates and conditions, which reliable/reputable gardeners will additionally keep documentation on for you. If it was a hybrid strain to begin with, try to find out what varieties were used to create it. Most seed companies guard their hybrid "recipes" to prevent anyone else from profiting off of them, but it never hurts to ask.

Watermelon vines often thin themselves to some degree, but in many cases, removing excess fruit can result in a better crop. If the vines flower early, before they produce significant foliage (if I understand your post, this doesn't sound like your vine's problem), you can remove those early flowers to delay fruit set and encourage extra growth (needed to support the fruit later on). Once the vines start producing fruit, wait until the fruit is about golfball size before removing it. Removing smaller fruit (before the vine aborts what it considers excess fruit) may be counter-productive. The number of melons a vine can support will vary with cultivar, weather, etc. So, leave your vine alone for a little while until it sets fruit and the fruit gets golfball size. Then, remove some fruit if you think there are too many melons.