Hi Nicolas
just looked at the video and its a capacitive sensor with an operating range of 1 to 25 mm
the n/c hall proximity switch that came with my tachometer module switches when the magnet is about 10 mm away
I expect your switches will be very similar but when you take for the gantry to stop as you say the gap has closed to 3mm or 1/8"
how about turning the proximity switch by 90 degrees so the magnet passes by end of the switch
John