IMO, the obnoxious behavior that you are using as a marker that neutering is neccessary is something that effects the human more than the dogs whereas the anxiety issues are something that seriously impact the dog but don't necessarily always reach a level where they significantly impact the human. No one can give you a garuntee that neutering will make a difference even if he were humping everything in your house there is no garuntee that neutering will change that behavior. My male still humps when my girls are in standing heat. If you are waiting for 100% assurance to make a decision you will never get it.
My experience with DAP is that when Nicky's anxiety levels were low it helped, during breeding season it took the edge off but he was still losing weight and demonstrating anxiety behaviors.