I did not miss your point at all.
You are completely mixing two issues here, the discussion here is about a turbo shaft engine and not a turbo fan. The elevation here is contributing to lower barometric pressure,
p = 101325 (1 - 2.25577 10^-5x h)^5.25588
In Psia you are looking at 6.75 psia at 20k feet compared to a 14.6 psia at sea level. This lower density will lead to lower volumetric air delivery, which in turn would lower the compression ratio, and lowered power and torque output, apart from that due to lower barometric pressure available to generate lift, the rotor speed needs to be increased for active lift compensation. So at high elevation operating mode, the engine has pre heat ducts and step unloader to maintain a powerband ration that can provide the additional speed, but the same operating map wont be used when operating at lower altitude , this is your adaptive control system in the Engine. The engine operating map, torque, powerband, RPM and gearing ratio' are all the functions of LLID sensor of the suction manifold, and rotor hub manifold. The engine behavior is based of the these LLID values.
In simple words it won't behave the same a sea level compared to high altitude. Hope that clarifies it.