I wonder if quick fermentation is better for watermelon stuff, like if the quick formation of alcohol would help prevent bacteria from taking hold. Perhaps starting with a high-sugar strawberry must and adding the watermelon a few days into fermentation might help? This isn't my area of brewing, but it would make sense. Sugar helps retard bacteria growth along with alcohol, so just an idea.
Side note, depending on what bacteria causes the spoilage, boiling may not be enough. I frequently sterilize things in my kitchen, and 250F is required to get rid of the nasties with the higher heat tolerance. This can be done in a pressure cooker at 15 psi for 30 minutes (I usually go 45 to an hour). Pasteurization may work for plain juice with added preservatives (like asorbic acid), but whole fruit may add extra bugs that resist lower temps. Spores, for example, definitely need the high heat, which is why pressure canning is required for low-acid foods to prevent botulism. I have absolutely no idea what effect sterilization might have on a brew, but just a bit of information on boiling to kill everything. Also, I believe processing juice at high temperatures sets the pectin or whatever it is that causes permanent haze in the finished product.
All that aside, I'd suggest thoroughly washing and sanitizing the outside of the fruit before you break into it. The inside should be naturally clean, but exterior contamination may introduce problems.