Seems to me this should be doable from the tool's output, as you get the parameters required (ellipse coordinates) to calculate a z-score for every point in your dataset. Though it would be a bit of coding. Thanks for your thoughts.
Great point about R - ArcGIS, Steve Kopp reminded me to get on the upcoming Aug 31 Esri Training webinar Go Deeper with Data Analytics w ArcPro & R. They have been doing some really interesting things recently with R integration, which is great, why re-invent for GIS what are becoming very standard technologies and methods!
That MVN package uses Henze-Zirkler, cool beans! From Wikipedia article Normality Test
More recent tests of normality include the energy test[9] (Székely and Rizzo) and the tests based on the empirical characteristic function (ECF) (e.g. Epps and Pulley,[10] Henze–Zirkler,[11] BHEP test[12]). The energy and the ECF tests are powerful tests that apply for testing univariate or multivariate normality and are statistically consistent against general alternatives.
I think I'm going to like grad school better than last time around because internet.