.. and decided to play with the FMC. Eventually he set the cruise CG to 36% which resulted in stall warning activation and an altitude loss of about 5000ft in the stall recovery procedure ...
Are you sure that playing with the FMC can produce a stall ? That would be a very persuasive and authoritarian FMC, methinks.
First, what limits our performance on a specific takeoff? It is either accelerate go OR accelerate stop
.. along with a bunch of other requirements, some of which you have nominated in your following discussion ...
The five things the software looks at ...
The software should be looking at the whole gamut of limitations ...
The forward cg limit gives the rudder a longer arm thus greater moment and a lower VMCG which may allow you to lift more weight out of an airport if VMCG was driving your limit.
That just might be arrant nonsense ? Perhaps you might have a read of FAR 25.149
https://www.ecfr.gov/cgi-bin/text-idx?SID=8faf9fb87379344cccafed99b90a7419&mc=true&node=se14.1 .25_1149&rgn=div8
A little knowledge can be a dangerous thing ...