Hi,

I'll go with your option of the ????.

Did you have the rotors turned or at least scrubbed the rotors with a coarse sanding, flat spiral, flap wheel, mounted on an angle grinder, before changing the pads?
You can do this while on the car while spinning the rotor.
It's Easier if the calipers were off and hanging but that's up to you and the size wheel you use to do the back side.

It's called cross contamination. Pad material is embedded in the surface pores of the cast iron.
The old pads were or are not compatible with the new material. Even if it's the same brand name pad.
This is why they try to talk you into a rotor turn. If they can new rotors by saying they will be to thin if we turn them. They get an up charge like a funeral home!

The pad manufacturers are always changing their material formulas and can vary in shape. Some add grooves where before they did not and vice-versa.

I clean mine with a nice swirling pattern and remove any ridge on the inside or outside edges that might interfere with new pad seating down. I cut the outer ridge back to almost make a chamfer or rounded edge.

I will also take sandpaper, in your case, and flat sand the pads to rough them up. There can be a glaze built up from them not wearing just as easily. Next choice is change brands of pads.

Try that.

As far as the turning and it becoming louder that the other, well, I'm going to blame that on the turning radius.
One wheel will always be faster in any of those two directions. But my motorcycle experience says you don't lean as far going to the left through an intersection and you go a bit slower making right hand corner turns!
I got pulled over once,min my twenties, by the police for going to the right too fast, by his estimation. I just shrugged my shoulders and said that how motorcycles work! If you go too slow, you fall over!
He let me go with a polite shoulder shrug too!

My disclaimer on turning is Only true here in America or where left hand driven cars are sold!
(:-)

Phil