I am not in favour of supporting Kerberos directly. There are quite a few approaches:
To authenticate passwords against Kerberos, use the LDAP SASL proxy scheme to load it off to slapd, or use PAM (feature request to support PAM logins is open)
To support GSSAPI, rather use the RemoteUserBackend and load authentication off to the webserver, which will provide an HTTP header with the authenticated username
Directly supporting Kerberos is quite complex, and in my opinion does not provide any benefits, so having the user running AlekSIS get a service token and keytab is an unnecessary risk where security can also be handled by components further down the stack.