Finding outliers in multiple dimensions
Have you considered using the Mahalanobis Distance? It's can be thought of as the magnitude of a multi-dimensional Z-score.

The way I prefer to view the the Mahalanobis Distance is as the square root of the exponent of the Multivariate Normal Distribution. This is similar to the Z-score, which is the exponent of the univarate normal distribution before the square is applied. A big difference between these two is the Z-score is signed, while the Mahalanobis Distance is unsigned, which doesn't matter for finding outliers anyway. 

I understand you don't have normally distributed data, but sometimes pretending your data is normally distributed can have good results, so using the Mahalanobis Distance can be worth investigating.