I'm sure you feel a bit deceived by all the stash, but it sounds like he's trying to bring you up to speed a bit at a time. At least he's not trying to hide it completely, so tell him you'll give him a little credit for that.
I think you'll find that nothing will slow him down faster than positive encouragement, strange as that sounds.It's the forbidden quality of it all that's part of the attraction. Your way of dealing with this indicates to me that he's pretty much a regular guy, so work with that attitude. He's just a regular guy with an odd fashion sense. Dress him up, take him out, get him drunk, take him home and boink him silly. A couple times a month with that, and you should have a happy camper.
Just avoid treating this like a problem, instead of a hobby or a kinky thing. Maybe you're not totally turned on, but I'll bet not everything you like turns him on either.
There is no "her." It's just your guy, in drag. You might have to make sure he doesn't forget that, like a lot of people here seem to have. Like sissystephanie says about how his late wife saw him: "lady on the outside, man underneath." Slap him silly if he starts to lisp.
My authentic self is me... an obnoxious redneck. On occasion, an obnoxious redneck wearing makeup. :D