I have two general ideas. Steal them. I don't have time to implement.

1) Find innovative ways to reduce production costs. Production is expensive. Unimaginably so. This can be things like:
a) Redesign physical set equipment. Ex: Set lights are expensive; a single light can cost tens of thousands of dollars. Design a new light that takes advantage of modern LEDs or something, or that can be deconstructed to serve multiple lighting functions (beyond what exists today).
b) Design automation to replace physical support crew on the set. Payroll is an enormous cost. Ex: Invent a tracking system that would make the boom mic not require a person to physically move it around to follow the actors. Yes, mechanization would eliminate jobs - such is the nature of creative destruction.
c) Innovation in use of set design and photography to make things look much more expensive than they are. A shining example of this was how Orson Welles shot Citizen Kane. Another example is what Spielberg did with the nonfunctional shark in Jaws. For those two, you're probably going to have to check out a book to learn how they did it. And more recently the impressive-looking but cheap sets and photography in Underworld (2003). These directors did unbelievably good things with constraints. Find a way to systemize this. To study what could be made cheaper, look at films that cost way too much, and see how each shot could've been cut down to bare bones - the absolute minimum dollar amount required to make the exact same look and effect.

The most choking example of waste I've ever personally witnessed was on the set of Van Helsing (2004) in Prague. The entirety of Old Town Square was cleared, about a hundred security held people out around the perimeter, and giant cranes and lights lit a scene of Hugh Jackman leaping in the air. What was the end product that appeared in the movie, you ask? A two-second shot of Jackman leaping in the air above some cobblestone. The whole thing could've been accomplished on a 10' by 10' mockup of cobblestone in a studio, or a cobblestone street somewhere cheaper to rent the entirety of than the Old Town Square of Prague.

2) As mentioned elsewhere in this thread, marketing costs are gargantuan. You have to get eyeballs on your enjoyable entertainment.
I watch independent film. The difficulty of going into a little-known film, even one that's received some good notice, is that I generally don't know a thing about it.
People enjoy trailers. Create trailers. Once production is complete, making a trailer for it is essentially free - it requires the software you used to edit the film and your own time and effort.
Run strings of trailers for unknown films on IFC. Run a 30-minute block of 30 to 45 second teasers with links to the film's site, where you have the 2 1/2 minute trailer and more information. Get eyeballs on productions. Right now getting eyeballs on productions is forbiddingly expensive. Revolutionize it. Cheapen it.

I don't think innovating other entertainment will kill Hollywood any faster. You have to innovate the film industry itself. Every human culture throughout history has enjoyed watching performers enact a story, of some kind or another. Moving pictures of performers enact a story isn't going anywhere in popularity. There's a reason it's such a profitable industry. Technology has advanced to the state it's in today where moving pictures of performers enacting stories are easily viewed the world over, but I don't think you should think about changing the type of entertainment so much as the mechanics of the medium.