The best suggestions I have heard consist of two things:
- Clearly defined X-Prizes for private industry: First company to achieve X receives Y prize money, second company receives fraction-of-Y. The total cost of the X-prizes will be a tiny fraction of what a bureaucratic government effort would cost.
- Remove as many regulations as possible from private industry - let it be a "wild west". Example: plenty of people want to volunteer for high-risk space missions. Currently, worker-safety regulations cannot be disregarded, no matter how many waivers the people sign. Get rid of that - as long as people know what they're signing up for, the government should stay out of it.
The de-regulation bit also includes lots of other things. Just as an example, the endless environmental impact assessments required before you can build a launch facility. There are mountains of regulations that stand firmly in the way of actually making progress in space...