Quick way to switch inversions?

Is there a quick way to cycle through inversions for a chord?

Yes there is. A short tutorial on inversions is here and on custom chords is here

Yes, as is shown the link above, but you’ll have to adapt to Scaler’s nomenclature and other factors. Scaler will often change the name of a chord rather than showing it as an inversion. I asked for “custom names” for chords. The name Scaler gives a chord is related to what Scale is in use. I’ve adapted to Scaler and don’t really care what name Scaler assigns to a chord as long as the notes I want are played.