How can a layering violation in a protocol be fixed at the API level? An API is what it is; a good API atop a gross protocol is only lipstick on a pig.

I think he's saying that you could potentially have the prioritized output without "HTTP2 know[ing] about progressive JPEGs". E.g. specifying "these layers are high priority" versus "the first n bytes of this stream are high priority": The first would be a layering violation, but I don't see any reason the second would be (not saying anything about its practicality). Now obviously the protocol would need to support the second (at least to use it in the context we're talking about), but I read the GP as using "API" figuratively enough to encompass this.

Yes.

And would pushing chunks actually require a protocol modification? AIUI http2 push mirrors the hypothetical request headers. So it could essentially push a range-request which the browser could use to partially populate its cache.