As you suggest, the most “Bayesian” answer is to not do this and the documentation regarding the MAP reflects this. But if you must, then you need to select an estimator and do so considering how collapsing your full posterior into a single point estimate will influence downstream inferences. Your tolerance for different kinds of consequences should shape what estimator you ultimately select. The mean, median, and mode, for example all reflect different loss functions. Keep in mind that some of these estimators may seem more reasonable assuming “well-behaved” distributions (e.g., symmetric, unimodal, etc.) but that posteriors aren’t always so cooperative.
We had some related discussion here.