What style of rotor, and what style of caliper and mount?
Is this a fresh install, or a system that has been on the car that has never been right?
The reason I ask, is some of the one piece hat/ rotors don’t take much heat at all to get “cupped”.
This will give you a squishy pedal until the rotor and caliper flex enough to get “square” pad contact. Any condition that causes the caliper and rotor not to be in perfect alignment will result in what you describe. High pedal effort is a pedal ratio or bore size issue. The two symptoms you describe tells me you have two separate issues.
The fact that pumping the pedal with the system closed doesn’t seem to affect pedal height, tells me you have some flexing going on at one or more of the caliper/ rotors, not an air issue.
Secure the rotors with the wheels off. Have someone watch the cal/ rotor while applying/ releasing the brake. If anything moves other than the brake pad, then you’ll have to get the issue sorted out.