Not knowing the local market super well... but what about a broadway venue? That's the type of thing people would come specifically to DtD for and not necessarily tack on going into the parks.
I like that you are thinking outside the box here, but SoCal has no shortage of world-class venues to perform Broadway shows. Aside from all the different venues in nearby Los Angeles that a lavish world capital like that has, Orange County as home to over 3 Million people and one of the wealthiest counties in the nation has several venues that host traveling Broadway shows.
The biggest is the Segerstrom Center for The Arts about 15 minutes away from Disneyland in Costa Mesa. Segerstrom Center has a 3,000 seat opera house, plus a 2,000 seat concert hall, and several smaller 500 seat theaters on its campus, in addition to art museums, rehearsal space, a ballet school, education facilities and learning labs, etc.
The traveling Disney shows from Broadway; Lion King, Mary Poppins, Beauty & The Beast, etc. usually perform in the 3,000 seat Hall that is noted for its dramatic modern architecture with angular balconies.
Although the Segerstrom's newer 2,000 seat concert hall next door has also hosted Disney-themed performances by Philharmonics and celebrity musicians.
And on the Segerstrom Center campus, or within a short walk, there are several very elegant fine dining restaurants, plus apres'-theater bars and bistros, etc.
Leatherby's Cafe Rouge is just off the lobby of the concert hall and is a popular spot for locals even on nights without a performance scheduled in the hall.
Point being, Orange County already has venues for lavish Broadway shows fully covered. Most mid-sized cities in America would kill to have a Segerstrom Center for themselves, and a few big American cities don't even have that type of offering on a single campus, and/or certainly not as stylish and well planned.
Downtown Disney Anaheim will need to go in a different direction other than "Broadway Show" venue. And the locals wouldn't give up the Segerstrom Center anyway.