first of all...don't keep the engines at 75% N1, that's ridiculous. Rather have them at 95%.
No Airliner in the world climbs at 75% N1 so I don't see any reason why you should do it.
The N1 has to be high here since the fan generates most of the thrust, especially in climbs.
But lets' be more specific. A turbofan engine is as most efficient at high altitudes AND when their compressors are operating in high RPM's, approx 90-95%. You wont reach the engines optimal gas flow condition(=Best specific fuel consumption) with an N1 speed of 75%...
Yes the air gets thinner, but just gradually reduce the rate of climb, but it's important to spend as less time as possible in the climb, because the fuel consumpition actually DECREASES as higher you go, due to the higher propulsive efficiency of the engine. To top it off, a jet engine is optmized for high altitudes, in high speed conditions and high engine speed RPM.
And to switch to mach at 20.000ft is not really correct either.
There is no set altitude when to do the IAS/Mach switch over, when to do it usually depends on temperature.
An airliner has 2 speeds for a climb, one in IAS (like 290kts after 10.000ft) and another in Mach (0.78 for example)
So you will simply fly the 290kts until the the mach number reaches 0.78 (it will as the temp drops as you get higher up in the air), when the actual mach number is equal to the mach climb speed you just switch from IAS to Mach, simple huh
