We have an update script from 2.3.6 --> 2.4.2, but not from 2.4.3-->2.4.4. As demand for this is not that high, it's probably not going to be written any time soon.
However, given your clustered deployment, upgrade is going to have to be handled carefully in any case. I think the best way to upgrade would be to setup a new cluster using 2.4.4, and tactically move over data. We can help document a procedure for this.
You'd have to migrate over
1. user data
2. OpenID Connect clients / SAML SP
3. custom LDAP schema
4. customizations (forms, css, libraries, etc.)
One thought... it might pay to wait for Gluu Server 3.0.0. This version is in QA right now, estimated release is 1/1. Because it's so soon, it might pay to wait a little bit.