I feel your pain. I've also found the GRX brakes are really hard to set up. There's hardly any clearance to work with
The "loosen calipers -> squeeze hard -> tighten" never worked for me, nor does using an alignment tool. That usually doesn't even fit in between the calipers and the discs.
Assuming the brake mounts are faced properly and the rotors are true, just take your time. My procedure is to slightly loosen the caliper, adjust it by hand while slowly spinning the wheel, then *slowly* tightening the calipers as you hold them into place. I've noticed that even while tightening the screws, the calipers tend to move, no matter how hard I try to keep them in their place.
I should also note that I tend to bleed the brakes until they are really tight. If you're doing the same, you could try underbleeding them (just let out a tiny bit of fluid at the caliper end), then resetting the calipers.
I'm currently waiting for an update to the GRX group. The new Di2 groups have more pad clearance, so I assume the next GRX will have it too.