[not downvoted - I'm happy that people are thinking about and exploring options like this, even though I don't think this particular application is very compelling. ]

I think Elizabeth has given the primary reason that this won't work - neither of the problems you list (expensive and often not replicable) are really addressed.  Those are problems with refereeing and intentional scarcity/prestige mechanics, not with a lack of auditable sequence of events.

In fact, most of the papers I read are freely published via a very simple mechanism: preprints on the author's web pages.  I don't worry that they're not bit-for-bit identical with what the relevant journal published, nor that there's some fraud about when something happened.  

Is hosting or fear of post hoc editing a blocker to open academic publishing? My impression is no, and if it were there are cheaper solutions.

Current publishing norms are kept in place at least in part by prestige dynamics, do you have a plan for addressing those?

I don't really disagree with any of that, but yeah I think you might be missing the issue of curation, which is kind of most of the work that journals do.
A revolutionary publication, before being widely recognized, will look just like an error. Most of the time, it will turn out to be an error. Fully evaluating it takes time and energy, and if no one is paying reviewers to do that, it's generally totally unrewarding work and no one will do it and the diamonds in the rough wont be made discoverable.
If you understand why we must reward the boring work of replication, you will also understand why we must reward the boring work of reading probably-bad submissions from unknowns and writing thoughtful reviews/recommending them for promotion in different lists.

My tasteweb [LW · GW] will help a bit with curation, but it's essentially a way of using voluntary moderation/curation work much more efficiently, the rewards for contributing are immaterial, sometimes nonexistent, sometimes negative (popular curators have to deal with a lot of moderation issues). I think it'll inject a lot of life into academic dialog, but I don't think it will be enough to fix academic publishing. It might fix publishing/discoverability in a lot of other aspects of life where the entities being curated aren't so hard to judge, though.
I haven't thought much about compensated review processes, but I always feel the issue looming on the other side of the hill. It's not going to go away.

By the way, do you know about dSocialCommons? It grew out of twitter's social network federation project, but the discord has become a bit of a meeting point for our sorts https://dsocialcommons.org/