I agree with the folks that think you should thin more, but I think the tree shape is the real problem. I’ve read recommendations that say one peach every 4"-8" of branch.
I think your main scaffold branches should have been headed back (and maybe you can still do that). The vase shaped trees in fancy places have scaffolds and branches which are bench cut (pruned to an outward facing bud or shoot) every 2 to 3 feet. Yours kind of look like 3-4 leaders with branches coming off them. I put some videos below which hopefully illustrate what I’m talking about.
You can really take off a lot of a peach tree and it’ll grow back assuming it started in reasonable health. I took off scary amounts of three mature peach trees I have and was sure I’d killed them but they look all bushy and happy now.
Here is one of my favorite videos about peach tree pruning. @Olpea made it and you have to ignore the parts where he says the video is bad! It’s one of my favorites! He shows scaffold selection and then cuts each scaffold and any branches way back to an outward facing branch. It looks like he leaves less than 2-3 feet (more like 1.5 feet):
@JAF Along with the video above I really like the two NC state ones below- just in case you haven’t seen them yet or @Olpea’s I’m tagging you. There is one more NC state video, “young peach tree”, but I found that one pretty confusing. I ended up just letting mine grow 1st summer and then selecting scaffolds and shaping second summer like the video above.
two-year old peach tree:
mature peach tree: