I think you have some work to do on two fronts - you have a trust issue that will need to be repaired, but you also have a decision-making issue that needs some attention. You seem to have fallen prey to applying solutions when you haven't clearly identified the problem. I'm guessing that someone had the idea to do 360s without a clear understanding of why, so you went the easy route and found that it did more harm than good.
It is so easy to do that these days; we've all done it. There are solutions everywhere promising astounding results, however unless the solution is exactly the right one to solve the real problem, the outcome is iffy, at best, and could be dangerous.
Recent research in neuroscience tells us that attacks on status, certainty, autonomy, relatedness and fairness (David Rock's SCARF model) generate a reaction in our brains that is as powerful and biologically similar to physical pain. As an organization, everything that gets done gets done through and by people, so why would we ever embark on a process or program without being as sure as we can be that, whatever impact it has on the people, it will also have an outcome in solving a critical business problem.
That said, I would suggest approaching your trust issue as a real business problem, doing good research to understand exactly why it exists - beyond the obvious, because if there weren't already a crack in the organizational relationships, you most likely wouldn't have felt the need to take on 360s. Get to the root cause - is it leadership effectiveness? Does your rhetoric match your actions? Do your processes align to the culture, and is it the culture you want?
Once you have identified the root cause, you can not only begin the search for the right solution, but you have your measurement indicator that will tell you if the solution solved the problem.