Done!

For posterity, here is the process I've used:

- Add the following to .dir-locals.el:

--8<---------------cut here---------------start------------->8---
((org-mode
  (org-texinfo-classes ("guix"
                        "@documentencoding AUTO\n@documentlanguage AUTO"
                        ("@subsection %s" "@unnumberedsubsec %s" "@subheading %s"
                         "@appendixsubsec %s")
                        ("@subsubsection %s" "@unnumberedsubsubsec %s" "@subsubheading %s"
                         "@appendixsubsubsec %s")))))
--8<---------------cut here---------------end--------------->8---

- Add "#+TEXINFO_CLASS: guix" to the Org document.  This fixes the
  section mapping.

- M-x load-library RET ox-texinfo RET

- C-c C-e C-b i t (or "M-x org-export-dispath", then enable "Body only"
  and export in texinfo).

The result was really good and needed only a few minor changes:

- Add/remove some @node where it makes sense.
- Remove the @menu entries.  (Can this be set in the export settings?)
- Change the @uref to @xref / @pxref.

Cheers!

-- 
Pierre Neidhardt
https://ambrevar.xyz/