Very narrow gap between pad and brake rotor

I have just retired my Tektro brakes (13 years of service) and replaced with a pair of cheap Shimano MT200.

I have a problem with extremely narrow gap between the disk and pads. The gap is so narrow that it makes it near impossible to adjust brakes for no rubbing. Also any amount of dirt that gets on the disk during winter ride is guaranteed to cause a lot of noise.

Brakes don’t appear to be overbled. Pistons can be pushed all the way back into the caliper when pads are removed. Also lever freestroke distance appears to be usual. For contrast I compare this to another bike that has SRAM brakes on it. Lever travel is about the same but SRAM brakes have about 3x times as much of a gap between pads. It appears that for the same amount of lever travel SRAM calipers advance/retract 3x distance of Shimanos… This cannot be right.

It is difficult to take a picture of but here is a sketch:

What I have tried and checked so far:

Wheel off + pads off + push the pistons all the way back.

Makes no difference. Calipers can be pushed all the way in without a proble, Leveler bottoms out. After doing this, the bite point is lost and it takes a few pumps of the lever to let the calipers adjust and "find their place". After calipers are in place, the problem is back – gap is too narrow.

Re-bleed

I am no stranger to bleeding brakes. Done everything by the books. But for this particular subject it is important that I bled the brakes with pistons fully pushed back and largest bleed block (that fits) in place. This should make sure that the system is not overbled… I obviously don’t pressurise the system.
No improvement

Rotor thickness

My rotors are original from Tektro and I thought that maybe rotor thickness is different between Tektro and Shimano, but it does not appear so. Rotors measure 1.8 mm with a digital caliper…

Caliper tilt (pad not parallel to disc that makes visual gap smaller)

Nothing to say here, calipers are mounted straight. I readjusted them a few times.

Running out of ideas here. Any advice appreciated.