I went through a similar process trying to managewith separate menus for each website but found this was hard to manage and did not work well for several reasons.
Virtual Domains now has a menu filtering option where you can now have one main menu and choose which menu options are associated with each website.
Virtual Domains also enables you to specify a home menu item for each website.
In practice, this seems to work much better and is easier to manage.
Menu filtering works with multiple menus, if needed. I find it useful to prefix menu names with a code for each website to help remind me which menus apply to each website. (see below).