Here's what I did. "Works for me" as us programmers like to say.
I have the two versions installed in:
C:\Program Files\Freescale\CodeWarrior for Microcontrollers V6.1
and
C:\Program Files\Freescale\CodeWarrior for Microcontrollers V6.2
Copy the old DLL:
unit_cfz_v1_version_327.dll
from:
C:\Program Files\Freescale\CodeWarrior for Microcontrollers V6.1\prog\P&E
to:
C:\Program Files\Freescale\CodeWarrior for Microcontrollers V6.2\prog\P&E
Edit:
C:\Program Files\Freescale\CodeWarrior for Microcontrollers V6.2\prog\P&E\ngs_devices_cf.ini
In this section of the INI file for the JM128, I changed the name of the DLL from ...330... to ...327...
[MCUID7003]
DRIVER=unit_cfz_v1_version_327.dll
DEVICENAME=MCF51JM128
NUM_PACKAGES=0
TRIM_TYPE=0
That' it. For what it's worth, the BDM on my DEMOJM board is at Flash Version 5.79.