Thanks for your tests.
I will see if we can tune the behaviour a bit - however an excursion of 0.1 Mach is not unusual when the autopilot flies the plane.
Also keep in mind that 0.8 is a VERY high speed for a 737-300 to be flown at. Usual cruising speed is .74, and we flew .78 if we were really in a hurry.
The FL CHG pitch mode is also limited by the g-load it will place on the passengers. At very high speeds, it can not "pull up wildly" to fight an overspeed situation, this would be very uncomfortable. In fact a lot of real pilots will refrain from using FL CHG mode in these regimes (high alt, high Mach) because of the exact reasons you describe. Very steep descents, low pitch.
Cheers,Jan