HTTP headers must be written before the body; so once you start writing the body, you can't switch back to writing headers.
Server-sent events appears to me to just be chunked transfer encoding [0], with the data structured in a particular way (at least from the perspective of the server) in this reference implementation (tl,dr it's a stream):
You understood correctly; I was mis-informed. Today I learned about the "Trailer" header. I'm curious how HTTP clients handle that. A client like window.fetch will resolve with a headers object-- does it include the trailers or not? I'd have to test it out.
Which seems to be what you need to send 'headers' after a chunked response.