We have two peach trees,that were hear when we moved in (10 years ago) and sad to say they are the same as yours.
I don't think thinning the fruits helps (much).I think they (yours and ours) really need to be up against a wall to get the real blast of heat that they need to fruit well.
I was talking to the gardener at a local stately home a few months ago,and even there,where they have a walled garden,they don't always get a large crop of fruit.
I don't know where you live,but we are in the warm south east (near Rye) and if we can't get them to eating stage nobody will.
These websites give more information,but tend to confirm some of what I have said.
http://www.fruitexpert.co.uk/PeachTrees.html
http://www.telegraph.co.uk/gardening/howtogrow /3349116/How-to-grow-Peaches-and-nectarines.ht ml
http://www.allotment.org.uk/fruit/peach-nectar ine/index.php