Thanks, that's far more useful. I can avoid those problems, mostly, and some is just poor description on my part. Based on what you're saying, I think I can do exactly what I want to do, I just need to do it a little bit higher in the tree.
If it eases your mind any, the shed I built is so ugly there's no way I can sell the house without having it bulldozed and carted off. If I hadn't attached the shed to the tree, I would take it down completely. I think with your advice I can keep it looking decent enough for the life of the shed.
The water spouts process already began when I took off the lower branches to make room for the shed. I am going to select a few of those to keep the tree alive and clean up the rest to prevent the broom problem. Then, if I get the healing I would like, I will alternate harvesting those branches on a three year cycle.
Or if it doesn't work I tear it all down, and triple my garden footprint and make my wife happy. So win win!