I'm really glad to hear this effort is underway to move towards real, actual web apps! Having worked on the Music NGA rewrite, I can say that much of the necessary work to facilitate this transition should already be done for the Music app. The biggest hard-dependency the app had on legacy mozApps that may still be an obstacle is the DeviceStorage API. However, since the backend is abstracted out via ServiceWorkers, it should be relatively easy to substitute DeviceStorage for something else like maybe IndexedDB or even a cached copy of a cloud-based storage provider.
I believe when we landed Music NGA on master, we shipped with ServiceWorkers OFF by default when building. The backend was done in a way that sort of "polyfilled" the Fetch API if you build with ServiceWorkers turned off. So, you may need to build with a flag to get a SW-enabled version of the Music app (I believe the flag is "NGA_SERVICE_WORKERS=1").
If I get some time after the work week, I can take a closer look at helping with this transition. In the meantime, if anyone out there wants to start on this, feel free to reach out to me for any questions regarding the architecture, etc.
-Justin