Does "sola fide" have any Biblical support if Paul's "works of the law" is just referring to the Mosaic ceremonial law?

I've been digging into "the new perspectives on Paul" and thinking that many of the "new perspectives" seem like, or lead to, traditional Catholic/Orthodox perspectives on Justification. Specifically, the idea that when Paul refers to "works of the law," he is referring exclusively to the ceremonial aspects of the Mosaic law. This would seem to shatter all the Protestant go-to verses that supposedly prove sola fide. **TLDR:** If you read "works of the law" to mean works of the ceremonial Mosaic law (i.e., circumcision) exclusively, then what is left to support the doctrine of sola fide aside from Luther's Occam-inspired philosophy?