Welcome to the forum LabOwner2014,
I LOVE the DNA idea BD
But Really, no reason that YOU need to pay to have a strange dog's poop tested. Let the condo association fees pay. All you need to do is say that because you are a responsible pet owner, you always pick up after your dog.
But In order to prove this and avoid conflict, you have already tested your own dog's poop so that it can be 100% identified if need be.
Because some people are afraid of your dog, it makes sense to keep dooger close by, perhaps let people know that the dog is very gentle....just to get people more at ease and friendlier with the situation. (if this is possible).
Make the dog sit when they walk by so they see it's obedient and they are less fearful....might be a suggestion.
From loads of experience, lol - Living around strange people is a lot easier when everyone feel as little stress as possible. Good luck!