You describe a major problem in the pecan industry—predation by birds. A major legal concern for management efforts is the federal Migratory Bird Treaty Act of 1918 that protects most bird species, including blue jays. There are similar state laws that protect most birds.
We would strongly suggest that you implement non-lethal control techniques while applying for a depredation permit from your state's wildlife agency or the state office of USDA Wildlife Services. It is critical to act quickly when bird damage begins as large numbers of birds can appear, and the longer birds use a feeding site, the harder it is to disperse them.
Non-lethal techniques include propane cannons, cracker shells, hawk kites, netting, and Mylar tape. The flying hawk kites are very realistic and seem to work well in apple orchards. Mylar tape glitters and shakes in the wind and seems to scare the birds as well. Understand that all visual and acoustic repellent techniques have limited effectiveness. Birds can habituate to them very quickly.
More details on control are found below. You might get some ideas from how California jays are managed in pecan orchards.
Online Resources:
Scrub Jay Control
Bird Dispersal Techniques
