ESI requests don't send modified headers from req to backend?

[David Judd]

Working with Varnish 3.0.5, in vcl_recv, I set a X-Request-Start
header to the current millis since the epoch. I want that header set,
with the same value, both in the main request and in a resulting ESI
request (in part so I can use it to help match them.) But it doesn't
work that way--although as I read the documentation, it sounds like it
should. In fact, it seems that the backed only gets the original,
client headers when it receives the ESI request, and not the custom
headers I added before the ESI was triggered.

The provided example in this earlier thread appears to be essentially
the same issue:

https://www.varnish-cache.org/lists/pipermail/varnish-dev/2012-November/007385.html

Thoughts? Is this a bug? Is there a better way to send the same
timestamp for the main request and an ESI request?

Thanks,
David