There is. One publisher actually got mostly out of the publishing business and transformed itself into a digital repository/digital publishing vendor. While I realize this isn't exactly an open source solution, it does create a viable turnkey solution that fully supports the double-blind peer review process out of the box. I fully recognize that there are legitimate discussions to be had about Freedom and such, but I figure it's also worth mentioning that there are solutions out there that enable self-publication within the generally-accepted peer review system. The critical point here is that in order to gain recognition as an authoritative publication, it would have to be published within the context of an already-accepted organization. So, for instance, if the editorial board were to go to, say, the American Library Association and/or one of the top 10 or 15 LIS schools and were to relaunch a similar publication, it could probably work fairly well.
It's also worth noting that the field of particle physics has already addressed this issue, and made all their work open access. In their case, the major journals in question are being compensated by charging subscription fees to libraries (with a "gentleman's agreement" that libraries will pay), but I also know that one or two of the most prestigious journals priced themselves out of the game. This, I think, is increasingly going to become the model for how open access publishing will work, and how commercial publishers will be able to keep their doors open.