let's swash that buckle.

I suspect that 'invert/inversion' were terms that would have been used by the educated with access to the medical/legal literature on the subject, and quite possibly the German and French literature on the subject, rather than in any kind of common usage. A quick check on the famous 1881 gay porno Sins of the Cities of the Plain by 'Jack Saul' doesn't show up either term.