One reason why the higher CFM56 ratings are not certified on the shorter 737s is that, with the shorter fuselage, there isn't enough tail authority to overcome the pitch-up moment that you get with increasing thrust.
Since we've gone to FADEC, the 'overboost' available by firewalling the engine has been minimal (there is some "headroom" to make sure you can get to rated thrust even with minor air data sensor errors, but we're talking less than one percent N1) unless you select Alternate mode. As I've noted above, that may not be a good idea...