Resolved this issue with the help of Niclas from Pianoteq sales and support. What you need to do is select to manually activate the software with an administrator's account on each machine. Even if you've previously done the automatic activation, your registration number will appear in the manual activation process. If you have machines you need to install on for the first time, log into your Pianoteq account and see which serial numbers have open activations available and use those during the manual activation.
Here are the specific instructions I received:
"On each machine, launch Pianoteq and choose Manual Activation. Click on the 'Go' button which sends you to the Pianoteq website. Click on the 'Download Key' button. Put the 'pianoteq-key.txt' next to Pianoteq (that is, next to c:/Program Files/Modartt/Pianoteq 6/Pianoteq 6.exe).
This will allow any user of the system to use Pianoteq without the need to activate."
We're up and running!
Thank you, Niclas.