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.
I think I am inclined to try aeration and bacteria, maybe vacuuming, and other fish. If things get worse instead of better I will then get to try figuring out if the equipment is as big as I think.
My neighbor has the equipment to dig a second pond. He is digging one of his own right now. It's 12' deep. Moving the garden is a huge undertaking. But, we need to move it eventually because the huge trees cast shadows and some of the garden is shady. I figure we could place a swimming pond in the sunny area. And yes, it would be smaller, for swimming. We could more easily net it and clean it. Skimmers and filters would be more effective. But that's years away.
I am not thrilled with swimming with the leaches but maybe the population isn't too bad. A dock in deeper water would help with being able to swim, I think, without being bit! There are some steps I can take and hopefully DH will be willing to try a swim after these measures are taken.
Has anyone used a net over a pond of this size before? I think it would cost around $500 and we'd have to look at it. But it is a preventative option. I also have to get rid of those goldfish.