'Round here cotton seed hulls are used. In Ga. you should be able to find 'em at a feed and seed store. It would be best to know they are from organically grown cotton but I highly doubt you will ever find such. Cotton has a high pest problem, most native plants will, and thus is sprayed with all sorts of wonderful poisons ;o)
I would say those watermelons in the new beds are getting all they need. Its the plants in the older bed they need help.
You still have time to grow a nitrogen fixing plant like legumes, southern peas such as black-eyed peas are great, in the bed that you will grow watermelon in next season to help increase the nitrogen. Do not use the same bed as you did this year. Remember to use crop rotation.
You could also sow the same legumes in the watermelon patch now. I doubt if you'd get much benifit though as the roots must decompose to release those nutrients. Also you must know that legumes must not be allowed to develope seed or many of the nutriets will be transfered to the bean from the roots. Whack the legume plants before seed form or pick out the developing seed pods.
Mike