How can I sign in via a different linked Google account?

Adobe customer  has been less than helpful on this one.

I have a work computer and the school computer. Both of them have Acrobat Reader DC installed. I linked one google account for one of them. And I linked a different Google account for the second one.

Now that both computers are mine, I want to link both acrobat reader's to the same Google account. This is so I can take advantage of the cloud sync.

On the one computer I logged out, and then I log back in, and I choose the Google account option. It automatically assumes my wrong account. I try to log out and log back in using the other one. It always assumes the one Google account and I never have an option to select which one at any point in time. Does anyone here know how to fix it so it can work?

When I asked customer support, they recommended I uninstall and reinstall the application. This has nothing to do with the problem I told them. I did it anyway. It did not work. As soon as I try to login via the Google account the reader starts Safari browser and it logs me into the wrong account every single time.