Hi gtess,
I would like to confirm if you deploy Dirsync in the same forest. I have done a test on my side, and it is ok to install new Dirsync on another server and log on to it. The Microsoft Online Services Administrator should be an Office 365 global administrator. Could you try other Office 365 administrator accounts such as admin@domain.onmicrosoft.com? If the issue persists, to narrow down the issue, please create a new Office 365 administrator in Office 365, and use this credential to test it. Please feel free to let me know the result.
Thanks,
Johnny Zhang