I figured this out, and was able to fix the problem using AdminStudio.
1. When I created the AIP for 11.0.06, a new UpgradeCode was created. This needed to be added to the MSI under the "General Information" section.
2. The upgrade code was also missing from the UpgradeTable. Added the code and tested it out.
During the test, the previous version was removed and the new version installed successfully.