Term Reference Autocomplete field that searches fields besides name
As far as I've been able to determine, there is no way to modify what autocomplete searches in a term reference field, though if seems possible, even likely that there might be a module or hook that does this, I didn't find it.

To answer my second question, yes, making this an entity reference enables the use of views to power the autocomplete, at which point you can handle the formatting and search fields of the autocomplete.

Better answers on this are very welcome!