Sorry about the broken pipes. I doubt that copper sulfate would work long term. In my experience, only sealing the pipe will work longish term. Near trees, I would doubt tape would work for the long term, but what is "long term" for you?
I have done the slit pipe, glue, and clamp method, and I have dug up enough pipe to replace the problem areas. I prefer the latter.
PVC is brittle, so once you have poked a hole in it, it is likely to crack from those holes. If the pipe is low pressure waste pipe, and if you aren't going to drive over that area, you might get away with the slit pipe, glue, and clamp method. If it is under pressure, I would bite the bullet and replace the broken areas.
All the best,
Peter