I just set mine up over the last couple of days for my institution and I may be able to help, though I will first provide the disclaimer that I am by no means an expert. Here's what I believe:
The LTI installed system-wide works based on a single pro account. The configuration that you set affects Canvas through the pro Zoom account. Therefore all the accounts that use it must be licensed users within that account. Once they are, they will be able to activate Zoom in their classes and sign in no problem. (I say this because in order to install the LTI you have to have admin access to the Zoom account, though I could be completely wrong).It sounds like in your case your faculty are not users within a single account so I believe rather than setting the LTI up at the Canvas system level it will need to be set up at the course level for those individual instructors who want to use it.
I would recommend contacting Zoom, explaining to them your situation, and seeing what they suggest. (Then share what you find out.)
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