Ultimately the answer turned out to be that the product does not support this out of the box. LANDesk themselves use it, but it sounds like it's through the browser plugins and may not work with integrated login like we need it to. Also it would require consultant time to configure it because they have no documentation available to customers for setting it up. Disappointing but not unexpected.
There are lots of other service desk apps that have full SAML integration, including provisioning users, so hopefully this is on LANDesk's radar for the near future. As it stands now, this is a check in the "move to another product" column for us.