I don't see how this would resolve the issue, since teachers wouldn't know if you had a way to revert it to the old mode. (Which, by the way, you easily could, using the standard OS-changing method)
Short answer: there's no way to do it permanently, or in any way that enforces the inability to do non-CAS functions given a few minutes.
You mentioned the ability to install a CAS OS on the non-CAS nspire. That method also works just fine in reverse. However, it runs from the calculator's RAM rather than truly installing itself. A simple reboot would get you back into the CAS OS, taking around 15 seconds.
If your primary motive is to save money, you could consider buying a used calculator. You can find used ti-83+ calcs on amazon for around $35.