Hmm I've never been bothered by the word "provider." I think I like its neutrality and ambiguity, since a good companion provides many things (and providing for someone is admirable right?) But I see the point now about it being a little clinical. "Courtesan" always strikes me as stuffy and pretentious, although if someone sees fit to call me by that name, I take it as a compliment.
"Hobbyist" has always left me cold, although I agree that it's an accurate description for the way some men approach the exchange. Maybe "benefactor" is the male equivalent for "courtesan"? It's a shame there are no words for either position that seem to get it just right....