I can only call it as I see it, and the pattern of leaf yellowing looks more like Iron chlorosis to me, but it could also be a Zinc deficiency, there are subtle differences in they ways these and other mineral deficiencies manifest themselves, many are common to sandy soils.
What I would do is get yourself on of those cheap simple soil pH test kits and get some idea of the pH of your soil. The ideal pH for peach trees in commercial orchards is between 6 and 7.
Applying Chelated iron in the watering can is very effective when your soils are acidic (low pH)
I've attached a file from Victoria in Oz relating to some of the basic symptoms of mineral deficiencies in fruit trees, the basic rules apply to your trees as well as Aussie trees re foliage markers...having said all this it is possible that some fungal pathogen is at work.
I wouldn't remove any branches just yet, unless you are 100% certain they are dead, if you do remove them don't keep them in your garden/compost just in case fungi are present.
AG0089.pdf