Turns out the online documentation is just out-of-date. Using "--help" on the
CLI itself returns the following:

Browser ID:
  F  user-agent field sent in HTTP headers (-F "user-agent name")
(--user-agent <param>)
 %R  default referer field sent in HTTP headers (--referer <param>)
 %E  from email address sent in HTTP headers (--from <param>)
 %F  footer string in Html code (-%F "Mirrored [from host %s [file %s [at
%s]]]" (--footer <param>)
 %l  preffered language (-%l "fr, en, jp, *" (--language <param>)
 %a  accepted formats (-%a "text/html,image/png;q=0.9,*/*;q=0.1" (--accept
<param>)
 %X  additional HTTP header line (-%X "X-Magic: 42" (--headers <param>)

So the answer to the question is to use "-%X" or "--headers".