W3C published draft:
In w3c/ServiceWorker#127 it is suggested push API is incompatible with having multiple registrations per origin. That seems like a problem.
Another problem is it not defining the protocol between the browser-operated server and the site-operated server. That really needs to be included for this to be suitable for standardization.
Discussed in London; Alex did a review, and it is now on a good path.
Note that work on the protocol is just starting up in IETF.