I have more ideas in my other comments, but fundamentally I think open review is a better norm. Publish a preprint and let the world have at it! You don’t need a committee to decide who your ‘peers’ are: if they care enough they will be reading your paper anyway. Normalising publishing these reviews (like PubPeer) would ensure review, without an arbitrary choice of ‘peers’. Think a paper needs more reviews? Then pay the reviewers and publish their reviews. The benefits of secrecy and gate keeping are negligible compared to the downside.
Currently billions are spent on academic publishing even though servers are cheap and the labour is unpaid. This would be a good starting point to fund replications. But that will never happen while the status quo is “peer reviewed = good science”
Also, scientists should be spending time on what they think is valuable. Scientists happily replicate important papers using their existing resources. If no-one cares about your result and won't replicate for free, then pay someone to do it! This is the basis of adversarial collaborations (see FEP collaboration funded by a philanthropic foundation). No-one is advocating that e.g. we replicate newtons law for the Nth time. And how to determine if N is enough? Use Lakatos' MSRP to compare rival theories.
Again, these dreams are predicated on the status quo changing to where scientists care about the content of a paper, not where is it published or that a faceless committee has accepted its foibles. A world where the public response to a non-replicated result is:
"I wonder if any groups plan on replicating?"
vs
"New paper published in __nature__ has <newsworthy counter-intuitive yet unreplicable result>! Book deal / gov. contract / faculty promotion here I come!"