You can reframe almost any statistics as Bayesian if you try hard enough. That doesn't mean it's actually helping you. If you have a method for generating 'good' priors and it doesn't work, it does far more harm than good when you use that to analyze this kind of anecdote. Anecdotes are such weak evidence that the chance it pushes your priors into the correct result is super low. You'd be better off not trying. Just accept the need to gather proper amounts of evidence.

Or in other words: Some undescribed system of priors could help, but the system you actually described doesn't help. So "use priors" is a bad answer.