FD - I've not spent meaningful time working the 737NG, and the last time I did much detailed engine performance work was when we were still delivering JT9D powered aircraft. I do know that on the JT9D-7R4 powered 767 the TSFC curve went up steeply above max climb - not so sure about the CFM56-7 on the NG.
But the 737 has a somewhat unique feature. The 737-300/400/500 all used the same CFM engine but with different ratings - and the NG is the same way. You can't use the max rating on the shorter 737s because the pitchup moment is more than the tail can overcome (on the 737-300/500, there was an actual physical block that prevented full throttle, on the FADEC NG it's simply controlled by the rating plug). So on the lower rated -700 (or -600, although I think that's out of production) it's possible that max TO is low enough that you're not getting into that steeply increasing part of the TSFC curve - the answer might well be different on a 737-900ER.
BTW, I recall we had an issue years ago with one particular 757 operator that was having a rash of compressor related engine failures. Come to find out they were doing derated climbs, which tended to operate the engine in an RPM range that caused stator vane resonance and the vanes would fatigue and break
