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I would say that it is not unsurprising that you saw this growth pattern this year. By next year, they trees should have settled in and will produce a more normal growth pattern. You will likely need to do a little pruning though, to keep them in tip-top fruiting form. This article will help:
http://pubs.ext.vt.edu/422/422-020/422-020.html

Your trees have a disease called peach leaf curl. It is a fungus and, yes, copper fungicides will treat it. I also suspect that it may have peach borers. Pests are often attracted to plants that are already sick, so this would make sense.

Most copper fungicides are considered organic and are effective against peach curl when regularly applied, but, because I suspect a pest problem as well, I would recommend a spray called neem oil. It is organic, safe for people and pets and is both a pesticide and a fungicide. It will treat both the peach curl and the peach borers.

It is hard to say exactly what the problem is. But... Based on your information, I would suspect nematodes. They would attack the roots and would kill the tree over time, and with the extra added stress of fruiting, it could be enough to push them over the edge. The only way to diagnose nematodes is to have your soil specifically tested for this. You would need to ask your local extension service if they can test for it or where they would recommend that you test for it in your area.

The gel is often a sign of peach borer. It may be dripping from the borer wounds. This article will help: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm

Dormant sprays should actually be started in winter. Use dormant sprays before green tissue shows in spring buds. Use on days when the air temperature is above freezing. Use a Superior Oil spray for the first dormant spray application in mid- to late winter. Three weeks later make a second application of Superior Oil or Liquid Lime Sulfur.

When spraying trees to control peach borer pests, choose those with lindane endosufan or chlorpyrifos. Sprays should be mixed according to label instructions. They should also be applied so that it runs down the trunk and soaks into the ground around the base. Try not to spray on foliage or any fruit that may still be on the tree. The best time to spray trees is within the first or second week of July and again in late August or September.