This isn't a question about AAMEE, because I didn't use AAMEE to create this installation package. I used the Acrobat Customization Tool, as is detailed in my original post.
As far as the licensing logs go, there aren't any for Acrobat, as it does not get installed with the rest of the CS6 Suite. It gets installed by it's own standalone installer, made using the Acrobat Customization Tool, which is supposed serialize each system it's installed to. Which it does not seem to be doing, hence the issue.