From personal experiments, while adding a small quantity of vinegar to the broth doesn't give a strong flavor necessarily, it's a flavor/aroma that still seems readily identifiable. Obviously, plenty of people are perfectly happy with adding vinegar, so YMMV.
If you intend to experiment, I'd consider using any acid you'd happily add to a soup over vinegar. Lemon juice, tomato paste, some sauerkraut brine, or a splash of wine would all add some acidity without the potential for an off-putting vinegary taste or smell.
That said... It sounds like you're chopping the bones..? If so, have you considered using a hammer to simply crack the bones instead? If I were so committed (which I admittedly am not), I'd be inclined to put a dish cloth over the bones and just beat on them. With a long simmer, a few solid cracks should be enough. But that's also point where YMMV.