I agree it sounds convincing, IF your front end makes a thump noise going over bumps or into holes.
I keep forgetting that you say, "it is when I apply the brakes" and turns make no difference.

So, you are changing the pads back and forth, I hope you have lost those deeply angled pads.
Have you tried a completely different brand of pads and scuffed the rotor clean with a sanding flap wheel. I'm sure you have used a brake cleaner spray. Everyone loves that smell, DON'T YoooU!!

What you are describing by a grinding noise, of which, in most cases, has to be a rotation noise. For me a grinding noise that stops and starts continuously is a reciprocating noise or a severely warped type of repetition when it comes to brakes.

I only turn a rotors if I see colored or shiner spots that say "this is a hard area" or real deep grooving. Deep, being a lot more than just a few thousandths deep too.
If you have some warpage or run out, turning them can make them worse to have it again, as they will be thinner. Turning them nowadays cost about one third of a new rotor so I factor that in.

You said the rotors were recently replaced. Could they need to be turned now a little? Do you think they are a decent grade rotor since they have some miles?
What you say or have a picture?

I also use a angle grinder to remove any lips from the rotor that stick up above the plane of being a flat disc.
These appear mostly on the outer rim of the rotor after many miles of running. They can keep a new set of pads from seating right away.

I can say I had a problem with a set of pads. They had gotten worn only about halfway and would make a groan or even a howling sound vibrating through the front of the car.
They seem to glaze right back up after a cleaning I would do.
My term Cleaning means sanding the pads with the coarsest grit I have and cleaning the rotor and leaving a shiny swirl.
I ended up just giving up and tossing them.
This was many many years ago and as best I can remember, they were a Napa boxed pad. This was even before pad warranties. I wrote it off as the brands recipe of materials in the mix.

I have not heard of calipers doing anything close to this except when halves are a mismatch.
You might want to check the for those dimples to be matching.
Maybe you have a very special breed of caliper? (:-) Nah just kidding.

Sure wish I could help more but I'm stumped or just don't know which way to jump.(:-)

Phil