At first I thought a Multisite installation would be a good solution, but exporting individual sites from multisite to another host is rather complicated. Perhaps individual subdirectory staging sites do make more sense. In order to have a single login, the individual sites would need an auto-login scheme triggered by an appropriate nonce included in the forwarding request from the landing site which put up the initial login.
After verifying the nonce, the user can be logged into a specific site by code without a password with wp_set_auth_cookie(). This could be done through a custom landing page on each site. When it comes time to export the site, remove the page and related template, which removes the auto-login functionality and the site then requires individual logins as usual.
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