Members area with externally-managed htaccess / htpasswd authentication?

Does a double install sound feasible and the right approach?

Given your restrictions, yes…I can’t think of any other way to do it with a single install. If there was a way to get the legacy software to control member accounts via any other system (perhaps dumping to a CSV which can then be read into a MySQL table via a script?) then you would be able to take advantage of some techniques to control WordPress users via external database tables or write the users directly to wp_users via script and the wp_create_user() function.