Two new ideas have been brought forward to fix this problem, both of which are actually good enough ideas that they should have been pursued even without the money problems.
1) Smaller ships.
2) Drone ships.
Both of these have value far beyond just increasing the number of ships for less money. I think that one of my most overlooked developments of the last twenty years is that no other state has started developing a conventional, peer-competitor navy to challenge us with. Most of the "possible competitor" states have either ignored their navies (Russia) or begun work on asymmetric threats (Iran, China) in order to neutralize the effectiveness of our capital ship intensive navy. Smaller ships and drones both help to tilt the field back in our favor. A flotilla of smaller ships make "swarm" tactics less effective against us, and drones can much more easily dog subs for far less risk.
Here's hoping that the Navy at least seriously studies both of these ideas.