Yep, that was indeed it. Added the wildcard cert to the gold image following page 13 of this document:
https://www.vmware.com/pdf/horizon-view/horizon-html-access-3x-document.pdf
We then made the change via ADSI edit via these instructions:
Deployed the new image and we're all set in our 7.2 environment (at least for internal access...still working on the external access issues through UAG). Unfortunately VMware support was little to no help with this.