I agree with MI-Roger
. You're going to look like a dork showing off you DIY job to your friends if the casing is installed backwards. Not to mention if I was a potential buyer of your house and I saw that backwards casing, I would run because I would wonder what other funny DIY tricks were hidden.
Just tear it down and start over. Sure it will cost you a few buck but we've all had to pay for our mistakes before. I've done things much worse and much more expensive than what you describe here. You'll be happier in the end when it looks right.