This recipe/idea is very similar to Pyramid Brewing's Apricot Ale.
50/50 2-row Pale & White Malted Wheat (possibly with some acidulated malt & carapils)
Roughly 5% abv
Guessing they use Wyeast 1010 American Wheat Ale Yeast
Pyramid probably uses fresh apricots, apricot puree, & apricot extract. With Watermelon juice though, you're getting more oxidation than usual, which causes browning. To preserve the red color, try adding a bit of raspberry or prickly pear puree/juice with the watermelon. They are not as easily oxidized and natural compliments to watermelon.
Instead of adding quarts of weak juice, I would look into how to make a concentrate so I could add about a cup of highly potent juice for intense color and robust flavor. The trick there is getting much of the water to evaporate, or be excluded, without boiling the liquid or leaving it out for days. Freezing the watermelon first could work. They do something similar with grapes to make sweet Ice Wine. http://en.wikipedia.org/wiki/Ice_wine
Another important tip is to use a juicer (not a blender) that is a low RPM masticating type, which doesn't whip air into the juice. You want it to press the pulp to extract the juice, taking care not to oxidize it like a high RPM centrifugal juicer would. Masticating juicers are also more efficient and extract more juice. If you must use a blender, pulse in batches on low speed and then quickly liquify. Strain through two layers of sieves (course mesh on top, fine mesh on bottom).