Best move would be to institutionally forbid, or disincentive somehow, publication in non open access journals.
In both cases, the policies (NIH in 2009, UC system in 2013) were shots across the bows of the large publishers, and permit a gradual easing of the culture without just blowing it up. So long as the eventual goal of all open-access is met in a relatively timely fashion, I think the strategy of slowly cinching down the rule is a reasonable compromise.
[1] https://publicaccess.nih.gov/policy.htm
[2] https://osc.universityofcalifornia.edu/open-access-policy/in...