Yeah, I hear you on not willing to cut down trees, especially an old apple! I am a big fan of trees, especially old apple trees. They seem to have a spirit of their own.
You are likely fine with a backhoe going over a leach field, just not the tank itself! The tracks do a good job of spreading weight out so they don't sink while working.
It is tough to consider harming a healthy ecosystem to rejuvenate a pond, I would have the same problem. However they recover very fast, and if done right will support even more life. That is why I suggested draining and waiting for the life in it to find a new home before liming it.
So it sounds like you have space to maybe put in a second pond? That may be a great option! Maybe make it smaller with the intention of swimming and easier management.
BTW i will swim in almost any body of water except one with those massive leaches, those things give me the willies.