when I see 737s ROTATING at 7000 ft...do you think that might be a problem?
errr no.
Have a look at figures 3.3.84
Granted that this is with CFM56-7B24 so 24K which is a standard de-rate for the larger engines. You need 9000ft BFL so being just off the ground at 7000ft ground roll is nothing new.
De-rate saves engine life, no questions there. GMI have on wing records which saves cubic $$$. Yet not all airports you can use it so no-derate for this departure, maybe you are runway or climb limited?
Boeing recommend on the NG no more than a 25% derate (Cant find the reference ATM) but given any runway contaminates or such most operators prohibit derate.