Update 2017: since GitLab 8.16 (January 2017), and issue 1376, you now can add deploy keys with write-access.
Original answer (2013): It is right a deploy key don't (and won't) have write access to a project (as mentioned in issue 2134).
That leaves you with:
- creating an LDAP generic account (if those accounts are authorized in your organization)
- creating a dummy account in a separate LDAP server (but the gitlab omniauth-ldap doesn't support multiple LDAP declaration).