Deactivated user, I haven't used Vimeo PRO either, but I did a quick search of their help area and found this:
Embedding Videos on Vimeo
The link above should direct to the FAQ, "Do I have control over where exactly my video can be embedded?" and gives instructions on how to "whitelist" certain domains. From your post, it sounds like you already know all this. 
The immediate problem I foresee is that if you're allowing the video to be viewed on the school portal, it can be viewed on any device anywhere that has access to the school portal. Anyone with video on their mobile device (in other words, basically anyone) can simply point it at the screen and record the video. The resulting copy will be low quality, to be sure, but that's the nature of piracy.
Is your experience with not being able to embed the Vimeo videos in Canvas specific to Canvas? Have you been able to successfully limit the domain(s) and embed the videos elsewhere?
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