That is exactly what I was going to say. Consult an attorney - the scumbags downstairs are creating a "hostile living environment" which you and your wife cannot endure. The scumbag landlord is making it possible by shirking his/her duty to you as a tenent. You have rights - make sure they are protected."Forced Eviction"...talk to your Lawyer about it, there should be some provision like it. It allows people to break lease agreements if living conditions are not agreeable to the point where the tenant feels that they can no longer remain...or something like that. I'm not a lawyer, but I had a friend way, way ,way back that dealt with a similar issue and her family Lawyer got her out by using some provision like this.
Re-read your lease. Chances are that it lists all grounds for eviction. Look for lease terms, or provisions for a notice to quit/vacate. Chances are pretty good your neighbor has the same lease. Look to help cement the landlord's case against him. Write letters to management complaining specifically about dates and times of incidents and demand action.
There's always the possibility that when the neighbor leaves the apartment, something BAD might happen to him. Of course, you wouldn't have anything to do with it, but its a cruel world out there.
But, bad things started to happen to him (bad karma and all that), and he eventually moved away..FAR away...Of course, I didn;t have anything to do with any of it, it was just bad karma (which sometimes needs a little help along the way.)