Boeing instructs to not use engine anti ice during climb and cruise with OAT or SAT below -40ºC.
Not sure if I agree with you. Boeing does not say not to use EAI below -40, they way I read it, it's not required to use it below -40.
I've been at FL 290 in clouds with OAT below -40 and slush building up under the wipers. EAI ON, please.
Engine anti–ice must be ON during all flight operations when icing conditions exist or are anticipated, except during climb and cruise when the temperature is below –40°C SAT. Engine anti–ice must be ON prior to, and during descent in all icing conditions, including temperatures below –40°C SAT.