Possibility of manually Re-Enrolling a device that has installing provisioning profiles blocked in the attached configuration profile.

We have a setting in our configuration profile on the student devices that prevents provisioning profiles from being installed. Unfortunately, as far as I know, this also makes it where we can't re-enroll devices manually. Is there any backdoor way that I'm not aware of to re-enroll a device without wiping the device first (I know I can perform an iCloud backup, wipe the device, and restore to backup)? Our devices were setup using DEP and Pre-Stage enrollments (Managed/Supervised devices), so they weren't ever used with Configurator making that method not possible either.