recover passwords from browser
Android browser should automatically back up any passwords on your Google account (the college email, but signed in on Google). The first step I'd try to recover your google account. 

Hopefully you had some alternative contact methods (secondary email, registered phone number, chosen account trustee etc). These allow you (sometimes) bypass password entry provided you answer any questions accurately enough.

In my last use of the recovery option asked me previous Google purchases and significant email communications and it let me in after 24 hours.

Beyond this I am unsure if rooting your device will be successful as major parts of the OS are