Nice closeups to ID the chips and components.
Looks like the only difference I see after quickly looking over the photos is the chip is marked with a different number on the third line. It may or may not be another chip, could be as simple as the same chip programmed differently -- perhaps with a battery type and serial number that can be reported to the radio. On the red battery, perhaps there's a flag or a model type that is reported so it knows that it's FPP-able. Might also tell the radio the battery chemistry if the nominal voltage is going to change slightly.
Now the trick is to try and swap that chip to the black battery, make the connections for a quick test and see if the radio will unlock the FPP functions. If it works, it proves you can get FPP to work on other batteries but you can't put that chip inside the radio to make it FPP with any battery. The best you can do is modify black batteries to be FPP but you'd destroy it in the process. My guess is that Motorola did this intentionally and probably wanted to have the battery be "smart" to some degree, being able to report basic info to the radio.
Next question would be, does a battery eliminator have this same flex in it, and if so, you could probably make a battery eliminator FPP-able if you can get into it without destroying it.