If anyone has a better method to install this application using a current version of Wine, or a more recent version Wine, then please post a comment. Here are my notes of what works so far:
The good news is that the key ingredients to success are the notes from a couple of people who had successful installations and they recorded the deeds on the winehq app DB section of the website. Of particular interest, was a "Gold" rating on an installation using Wine version 1.3.23 with a Windows XP winecfg and Winetricks ie6 (Internet Explorer 6). After loading ie6, winecfg gets set to Windows2000 and I had to run winecfg again to set it back to Windows XP before installing AAP9. I used Adobe Acrobat Pro 9.0.0 -- with a trial option selected (but I did not have time to play around with the Extended versions, presumably 9.0.0 would work as well) and the installation completed without issue when choosing a "Complete" install. To make that project manageable, I used "PlayOnLinux" which lets users download any version of Wine such as the one mentioned above, and it keeps everything nicely organized in subfolders. From there, I was able to copy over the entire registry (regedit / export) and the Adobe program installation folder in 'Program Files' to a current version of Wine in its virtual drive, and everything appears to be working so far. I was unable to get any other version of Wine to work for the install beyond the old version mentioned above. It is also possible to copy over the three (3) registry files in the root directory of the 1.3.23 installation on PlayOnLinux, but I thought that perhaps importing with regedit on the current Wine drive was safer. I also thought that creating the new Wine drive with a current version should also use Winetricks ie6 and a Windows XP winecfg so the registry matches as much as possible to the old version from PlayOnLinux.