Moving admin menu to site sidebar

I'd prefer to move all PunBB top menu's to my site's side bar. This worked fine for pages that use the main.tpl template simply by moving the <pun_navlinks> hook, but pages that use the admin.tpl template the "Admin menu" is inserted as part of the main content via the <pun_main> code hook.

Would it be possible to move the admin menu so that it is inserted by the <pun_navlinks> template code hook instead?