Also just thinking ... Are there any peach orchards or growers nearby to you? If so, maybe you could get some expert local advise. If your trees have the fungus the chances are others local to you also have it and maybe they found a good solution to prevent it's reoccurrance?
Something similar happened to My limes earlier in the year. At the time the tree was loaded and the weather was wet and hot, so I assumed the rot was caused by that. My fruit doesnt tend to get very big generally so i figure a few were on the overripe side for my young trees.
I picked as much that was close to ready and I dumped the affected fruit. New fruit seems good again now the temperature has dropped