I have done something similar with a previous project at work, though everything went through three layers, the front-end, which was reasonable as they describe

I have done something similar with a previous project at work, though everything went through three layers, the front-end, which was reasonable as they describe, the front backend, which just serves the single page's required data, and the back backend which was mostly the legacy version of the site's back-end but still had useful logic in it. Ended up working out okay, and the idea of each pages gets a service endpoint was a bit weird at first, but really gave it the flexibility to avoid needing to go touching the legacy layer very often.