I really don't think the result will or would have been any different if you had "introduced" the cats. They are outdoor cats, and they do as they please. By letting them outside unsupervised, both you and your neighbors are basically just letting nature take it's course, which is all about claiming, defending, and patrolling territory, so I don't really understand your neighbor's complaint either. The solution is kind of obvious from his point of view, or should be at least
The idea that either of you can make your cats "play nice" outside is kind of ludicrous imo. That ship sailed a long time ago.
To me the idea of scent swapping for an outdoor cat is pointless. Cats are very good at scent swapping on their own (by peeing on, clawing, and rubbing against things). The reason why you need to "help" them when they are indoors is that they are in much tighter confines, and you'd rather the cats not be peeing on everything. Outdoors neither is really a consideration.
If you are intent on getting another bengal, and intent on the bengal being an outdoor cat, then probably the best thing you could do is to get a spayed female, and then cross your fingers.