That cleanroom process has things in common with journal peer review, but it's a different process with a very different objective. As to speed specifically, I was envisaging a relatively small group of readers who are competent to understand the papers they're targeting and who are highly motivated to upset the journals, while journal peer review relies on a (hopefully!) wider and more diffuse group of people each of whom is a highly-cited leader in the area for which he or she is asked to review, and for whom a review request is a tiresome social obligation. So the cleanroom process would obviously be relatively labour-intensive (and thus slow) but it shouldn't involve the epic delays involved in begging reviews from scientific (or engineering) eminences.

As to which papers are important, for an effort like this to accomplish its objectives - bring some direct relief to the public, and bring some hurt to journal publishers - it's necessary to have a generally good sense of which papers are important or highly in demand, but not a perfect one. In particular, the objective in this case isn't to second-guess which papers ought to get published by journals or become popular with readers, but to give readers some papers they most want and take control of those papers from the journals.