Welcome
@Weedhopper
Muscadines / grapes require a lot of water and your low production during the dry period is most likely the cause. Transplanting is normally fairly easy but it must be done correctly. I have transplanted several vines in the past with 100% success. Be sure and transplant both the male and female vines if these are native plants. There might be someone here in the Forum that can give you step by step instructions, or I might suggest that you go to a vineyard website that explains how to handle Muscadines. Muscadines are different from "regular" grapes. Good luck with the transplanting.
As far as keeping critters away from the fruit, you could cover some of the vines with some netting. It is fairly inexpensive and easy to apply. A plastic barrier fence on either side of the vines is also an effective method for ground critters but not the birds.
Again