ASFKAP,
There is protection against N1/N2 overspeed on the B737 NG via the FADEC, the B737 Classic does not have such protection and overspeeds are possible and indeed probable in the scenario described in the original post.
Actually the CFM56-3 engines on the Classic do have protections of both core and fan. These engines have a N1 speed governing system contained in the analog PMC. Scheduling of N1K (N1 corrected) is set by PLA biased by inlet static pressure (PS12) and limited by inlet total temperature (T12). I have a block diagram of this PMC. The main output signal is a feedback error signal to the hydromechanical N2 control torque motor to trim the N2 demand. I gave the inputs signals in my original post which were N1, PLA, fan inlet temperature and fan inlet static pressure. This PMC does have but limited interface with the aircraft systems except for on/off function, PMC inoperative indication and N1 demand signal to the cockpit. The PMC also maintains a full function hydromechanical core speed control which governs core speed, schedules transient fuel flow and schedules engine variable geometry.
Now as you point out, the CFM56-7 engines on the NG are digital designs with much more sophisticated power management architecture, receiving quite a few more inputs and linking to aircraft systems which provide for more outputs.
I agree that you can indeed experience EGT overshoot on the CFM56-3 under certain conditions and reduced EGT margin as it is an engine reportable function not a controlling function per-se.
Regards,
TD