As you noted, SPGetCurrentUser "scrapes" the values from userdisp.aspx. Manager is not one of the fields available on that page. Instead, make a call to the UserProfileService, specifically GetUserProfileByName.
http://spservices.codeplex.com/wikipage?title=UserProfileService
M.
http://spservices.codeplex.com/wikipage?title=UserProfileService
M.