We have not had a Ken Holyoak smack down in a while, L&L Greg Grimes is a great source of information on this site and I consider him a friend but Ken is one issue we disagree on. I have Georgia Giants in my Putnam county pond and have had great success with them. With a .25 acre pond If you want bream I think Hybrid bream is a much better choice than Bluegills because of the lower fertility(Ga Giants do reproduce). Also in a small pond catfish can be your predator.
Is 300 Ga Giants to many for a .25 acre pond, not if some are going into the fry pan. If anything to many cats were stocked.
That said with your aeratetor you are not(imo) losing fish in your first summer because of over stocking.
What causing the die off, wish I could help there. Don't know.
BTW my Georgia Giants are now 4 years old and average 1.25 pounds with the largest being 1.5 lbs and no sign of the dreaded Green Sunfish.
Good luck