If you can use range officers as gun bearers, that would make it authentic, and you could do away with gun carts, too!
As the founder, your alias would be Dr. Livingstone, I presume? :-D
Seriously, as expensive as cowboy shooting can be, this could put it to shame if the rules required certain types of traditional rifles. There could be no uniformity to competition unless it was strictly big bore, as in over 40 caliber. Then, you'd have to divide into classes like double shooters and bolt guns, perhaps further divided into scoped guns. No quick action of falling plates to keep the crowds happy, either, as most of the guns used would be punching holes and crumpling steel, not to mention ricochet dangers that cowboy shooters with soft lead at low velocity don't have to contend with.
Paper targets would be harder to score for time, there would be no instant feedback for the shooters and spectators, so I can't see that catching on, either.
I'm not saying don't do it, but there are a lot of wrinkles to iron out. The best way to iron them out would be to simply find a few local friends that have the same interest, and start working out how you want to do it. That's how cowboy action started, just some bored shooters using their cowboy guns for IPSC or some such sport.