Bitter pit is generally caused by a calcium deficiency, but since your soil has plenty, it is probably due to an abundance of potassium. Honey crisp apples hyper-accumulate potassium, which blocks it's ability to take in calcium. So most commercial orchards will use foliar calcium sprays, even though their soil may have plenty.
The best way to remove excess potassium from your soil is to grow something which produces lots of above ground foliage then remove it. For example, growing alfalfa, then baling it removes 60 pounds of potassium for each ton of hay. Even better would be growing corn or sorghum, and then removing it while still green.