Minor fix: on the search results page, continue to show the admin/people/* tabs just as on the user search page before submitting to search for results.
Critical assistance spelunking through menu_local_tasks in menu.inc provided by Stefan Freudenberg.
Known imperfections: Menu tabs disappear on results page, that is admin/people/search/keyword lacks the list, permissions etc. tabs. Breadcrumbs are there and correct.