I commend you on trying to be a good neighbor (and a better neighbor than your neighbor who wasn't open and forward with you)...
Since you're trying to actually fix the noise issue I suggest having a bit of fun with your neighbor! I'd send a note telling them that you're in the process of trying to correct the noise issue and that you weren't trying to "shake" things up and present them with a box of these for the "inconvenience."
