I'm sorry you've got such a challenging pup. I'm glad you're choosing to look for help and advice and are willing to try things to help him. #1 I am concerned about the poo. Did the vet do a faecal test to see if he has an infection, or did he just prescribe antibiotics as a matter of course? You may want to have him DNA tested for IGS, an inherited disease that causes Vitamin B12 deficiency and can manifest as digestive problems early on. It's easy to treat if you know it's there, but untreated it eventually kills the dog. Although uncommon, the mutation IS present in working border collies.
I think your pup needs more structure. I don't think he should be allowed free in the house until he's earned it. Crate him unless you're taking him out to walk, toilet or play. You could also set up a secure x-pen if you want him to have a little more room. Take away the hundreds of toys and just give him one or two. Practice NILIF (Nothing In Life Is Free) - google it. Make him work for every thing he gets, his meals included. Be completely consistent and fair. He is now at the adolescent stage where he's testing his boundaries, and it sounds like he's used to very few boundaries. You will tire him out much more quickly by exercising his brain. If his attention span is short, help him learn to focus and keep your sessions short. Pop him happily back in the crate or pen after 3 minutes or whatever you can get. Even in a garden, if you can't reliably recall him, have him drag a long line so you can reel him in.
Good luck and please keep us posted.