Hi Kyle
A first guess is your class may be exceeding the WIFI capability of your school network. When "trying to connect via the code, the companion app will hang and not do anything" could be either than WIFI being overloaded or an issue with an individual project.
A second guess,despite your comment "so I don't think it's an issue there" is the issue may be coding issues. It depends on what "re creating usually have the same components and code" and the word 'usually'. Small differences in code and possibly audio or video files in individual projects , for instance, stored in Media can cause serious issues.
Something telling is that no particular phone appears to be 'glitched'. Has your school IT made changes to the network recently or are the student's projects getting larger, more sophisticated, etc. ?
If the second guess is right, you might be able to use App Inventor's alternate log in
Instead of #1, try having students with fussy Apps try #2. #2 does not have the time out restrictions of #1 but is not a substitute for possible less than optimum coding.
So if you can, try the alternative url if a Project fails . You can try to ensure ALL students are not downloading with QR code at more or less the same time if the network capacity is the issue.
Regards,
Steve