But moving it out of court and into an internal demonetization process has lessened the ability for creators to seek redress over spurious claims.

Would "seeking redress for spurious claims" be a practical solution? Which creators could use it?

If labels were forced to actually push these into the court system a lot of people would fold and settle but not everyone... those who actually got in front of a judge would likely win the case, probably even being awarded by the court for the prosecution having filed such a spurious claim.

Right now there is no cost to labels for submitting these AFAIK, there at least appears to be no cost even if the usage would be covered under fair-use.