Jerry Pournelle has done a lot of writing on the value of offering prizes instead of having the government foot the bill. We've seen some of that with the funding SpaceX gets, but the scale needs to be increased.
Offer $1 billion to orbit an unmanned (man rated) capsule around the Moon. Then another billion to land same capsule. $5 billion to land a crew of two, and return them to Earth. Since each is incremental, the risk for the companies trying to compete will be lower.
EDIT: Yes I know the costs are far higher than the prizes I'm mentioning. It's the general concept I'm aiming at.