Hi there.
If you only had one Artist license and you then upgraded that license to Professional you would be unable to use your upgraded Artist license.
However, it appears that you user account holds a number of Artist licenses. If you want to see exactly what you have just login at my.presonus.com and go to "My Products" then "Software".
Regarding your question "if I were to install the Artist version on a 3rd computer (if that were permissible) would it count against my Pro installations?"
It would not count against your Pro activations. It's important to note that you do not actually "install" Artist or Pro. The install is actually the same file regardless of which version you have. The difference occurs in "activation".
So when you open Studio One and it asks you to activate, you can choose to enter either one of your product keys for Artist or for Professional.
If any of this is unclear, please feel free to start an email support ticket at your my.presonus.com account under "Support".
