Now that the betas are all public, I suggest the following:
Instead of frequent betas followed by frequent releases, just make all the frequent releases betas.
On a quarterly basis, set aside a couple of weeks to put every hand on bugfix duty. Take whatever beta has the fewest bugs reported, clean up as many bugs as possible, disable functions that clearly don’t work, and then post the resulting, cleanest-as-possible verson as a quarterly “release version.”
Since releases and betas can coexist on the same system, this will provide users with a choice: a stable release they can use for production and betas they can test and go to when they need to use risky features that are not yet stable enough for release.