You may find that developing an LTI solution allows you much more control over exactly who is able to see which bits of data. A useful placement might be "Student Context Card" which allows a tool to be placed on the card that slides out when a teacher clicks on a student in a course.

Here my "New Test" tool is a local LTI tool that could display the data for a user. However this doesn't seem very good from a user experience point of view as a teacher would have to click through to each student (2 clicks) to find out their home campus.
Having a LTI tool that uses the Names and Roles service to display everyone in the course and then alongside display the home campus would seem like a much more usable solution.
If you are unable to use an LTI placement to display this additional data then there's the option of creating the LTI launch JWT from Canvas using an XHR call to the undocumented 'jwt_token' endpoint which you can then use to make an LTI launch to your tool.
https://github.com/instructure/canvas-lms/blob/a806980fb341b7cd91de73cd86be23ab6df7d231/app/controll...