Youve gotten the general culmination of solutions here, but I have to add onto one in particular.
My neighbors who have three large unspayed bullies, recently had to euthanize one because of fence fighting with my dogs. Theirs live outdoors full time and so naturally, WAIT next to the chain link fence for our kids to come outside so they have some stimulation.
I have an old one, a deaf one, and a bully with a propensity to start crap–if they all go out together, the bully will trot off with the other two and ignore it. If the bully goes out alone, he’s happy to rip roar along the fence with them, so needless to say I monitor it CAREFULLY. I just happened to watch the entire fight…I let my three off, they galloped off to the other side of the yard…three girls on the other side of the fence were running up and down waiting on the bully to run with him, but he wasn’t buying it…he changed direction and went to sniff a tree, and two of the neighbors dogs slammed into each other. In that much running/intensity it turned into a full on lockup fight. In the time it took me to get my dogs inside, get my cell phone and get over the fence to break it up, one of them was on the way to being destroyed. Didn’t have his number, ended up muzzling both girls and taking them to my clinic and footing the bill on my own because I couldn’t just let them lay in the yard until he got home. One girl made it, the other didn’t. It was AWFUL.
Anyway, neighbor agreed to fix the problem by doing what was aforementioned, adding a chickenwire fence 2’ in around the yard and planting bushes. When the bushes are full enough to be obstructive, I’ll pull the chickenwire down. Its worked beautifully so far…but I wish we’d done it sooner. I hope your solution fixes itself ASAP. If you have any type of relationship with the neighbor, I’d tell him a sob story to convince him to do something on his side too. Even dogs who get along well can trip/slam into each other and turn into enemies in that much barking and activity.