I figured out that I could get what I wanted with these three steps:
However, is there a less powerful role I can grant other than domainAdminRights. I would like my "user admins" to be able to modify contact details, create/edit distribution lists, and create new users. That's it.
zmprov ma email@example.com zimbraIsDelegatedAdminAccount TRUE
zmprov ma firstname.lastname@example.org zimbraAdminConsoleUIComponents domainListView zimbraAdminConsoleUIComponents accountListView zimbraAdminConsoleUIComponents DLListView
zmprov grr domain mydomain.com usr email@example.com domainAdminRights