Tough call. Your dog is like the new boy at school and has to fight to find his place in the pack. Or thinks he does. You probably remember exactly this happening when you were a kid at school.
A solution for fence fighting that I've read about is to plant stuff along the fence to prevent them getting so close to each other. Thick hedging for example. I have not had to do this but I do wonder just how long it takes for the darn hedge to grow to a size that is effective. And I think it would be best done on both sides so you'd need the neighbour's co-operation. Maybe another fence inside the main one?
I think your own idea is worth a try but will take some amount of time and effort from you and the neighbour. I can see your concern when you met the other dog loose. I have a Lab and my friend has a Kees and my small Lab is easily twice the weight of her Kees.
I do not agree that your dog is feeling aggressive due to pent up sexual frustration. It just doesn't work that way, dogs aren't horny all the time like teenage human boys.
They only get the urge when they can scent a female in heat. Of course maybe there is one in the vicinity that you are unaware of.
If you do consider neutering be aware it is not a sure fire fix all. One study using C BARQ data even says neutering may make dog directed aggression (and other) worse.
http://www.cdoca.org/downloads/files...20Behavior.pdf
And this study says it only helped in 60% of cases.
http://www.associationofanimalbehavi...neutering.html
Good luck. It's nice to have doggy neighbours yours can get along with, and vice versa.