You need to replace rotors when you replace pads...Are you on your second set of pads?
Excellent write up!, and also welcome to the site, I see your a new member.You might want to see if you have thrown a wheel weight, or rotate the tires front-rear to see if the problem changes before going after the brakes. If the problem stays with pulsation and the steering is still wobbly, then it is likely a glazing problem of the rotors. Truly "warped" rotors are super uncommon, although this is the general term that most people use to describe the problem.
it would be caused by pad material being unevenly bonded to the rotor. You must have gotten your brakes very hot at some point , more than a few times. Unfortunately it will not be possible to simply sand the offending glaze off. I have tried in vain on previous vehicles. In my case , I live near the top of an extreme hill and because of speed limits I have to ride the brakes almost all the way down (residential).
On my previous vehicle (2003 4runner) I was replacing rotors every 18-24 months because of pedal pulsation. It was as cheap to replace the rotors as turning rotors, which never fixes the root cause anyway. Even paying for premium rotors and pads made little difference, it was the weight of the vehicle and the conditions needed to stop a couple times a day every day.