Did you measure the dimensions of the LX "metal racks" to pretend that they are smaller?
My Rimowa carry-on measures exactly 55x40x20 cm (all-in; just measured it) and fits into the LX "metal racks" without any problem. And there is even a little bit of space left.

My experiences at ZRH on small aircrafts (Avro, F100) with carry-on gate-checkin:

In C: 2 carry-on -> no problems at all
In Y: carry-on were gate-checked for many Y pax when the flight was completely full. When the flight was not completely full, they only gate-checked the bigger carry-ons or those of people trying to take "half of their household" into the aircraft.

P.S. Nothing to pay when your carry-on is gate-checked.