No, a prize is a specific way to subsidize. In particular a subsidy based on goals set when the price is formulated.

There's nothing to stop the foundation paying it from raising its standards over time.

People -- at least, the ones sharing the transhumanist worldview -- want revival. The people who work on revival want revival. Revival is the goal, not a few piddling millions or billions of dollars. Industrial-scale revival won't happen until people are satisfied that it really is revival; then and not before will that huge market exist. When prizes are involved, you're looking at early-stage technology, whose only reason for existing is to become mature technology.