Hi Allan, one way of doing Inversionist is to hear the top note (which I find I do naturally). If the top note is the first note of the triad, then it is the first inversion. If the top note is the second note of the triad, then it is the second inversion. If the top note is the third note of the triad, then it is the root.
I'm sure there are other ways to do it, but this works for me
Cheers