TOA has both those trees in 5-6' feathered size. They ship very nice stock. Misterbaby. Here is a link that might be useful: TOA

I've seen similar type damage on my apples but had attributed it to scab either resistant to fungicide or surviving poor spray coverage. What's most noteworthy about the fungus associated with Brooks spot is it's resistance to sterol inhibitors so it would be present despite myclobutanil application. Proper coverage to include Brook's spot would then require multiple fungicides which would help also by preventing selection of resistant strains.

OK, correction; the apples on the branch are NOT King David, but Lady Williams (that's what happens when the Belgian Fence makes tracing the branch to the tag difficult). The King David in the hand are indeed runts, but excellent-tasting runts. I picked the Lady Williams today, also very nice, very marketable, but nothing close to King David. KD is still very firm when ripe, but in a pleasant sort of way, very sweet, with a distinctly winey taste, hints of Welch's grape juice, but also very spicy, appley, sweet-tart, matching the color. KD doesn't keep nearly like Arkansas Black unfortunately, but Lady Williams is reported to keep well and improve in ordinary storage, a plus where there is no refrigeration.

Do you remember where you bought it? You could try taking it back to the nursery and see if they can help you. Or if you ordered it by mail, send a picture to the supplier and see if they know what it is. I save all my plant mail order receipts for very much this reason.