If Jane has "the desire to stop drinking," she deserves a seat in AA meetings if she wants one. If she is disruptive by diverting attention from the primary purpose of "carrying the message to the alcoholic who still suffers," she should be tarred & feathered (kidding...but she should probably be steered toward NA).
I've known several addicts who attended AA meetings with no problem because they didn't broadcast the specifics of their addiction. They contributed great comments & gave great leads. Crucial that they didn't harp on the fact that it wasn't alcohol that brought them to AA for recovery. Some meetings are more tolerant of this grey zone than others. Conversely, surely there must be some serious NA folks in Jane's area....it just may take a while to find them.