To avoid more limb breaking, you should take off as many peaches as needed per branch. Usually, peachlets should be thin to one peach every 8-12".

You can prune a few limbs after harvesting or better in late spring. Don't do major pruning leading into winter. It weakens a tree and could make it more prone to winter injury esp. The fact that it can be very cold in NH.

Agree with rphc but given the time of the season and urgency of preventing more branches from breaking you could immediately prop all the overloaded branches with whatever you have available or can quickly make using a chainsaw and various hardwood saplings.

Thank you! I harvested a bunch, more fell off and the branches are happy. I am going to wait until spring to prune since it's already getting cold up here. For the winter I'll prop the lowest branches so that the snow/ice doesn't make them snap. Great idea!