Proximity Switches

[EddyCurrent]

The four you have are Normally Open type, the preferred type for limit switches is Normally Closed.
Also take note when you mount them, if you notice they use brass, stainless, polypropylene mounts.
The last two may be normally closed, it does not say, some of these just change a voltage level so that the input decides if it's on or off.

This manual shows the wiring arrangements but obviously for their own board.
http://cnc4pc.com/Tech_Docs/C31R1_USER_MANUAL_REV1.pdf

You could wire the sensors so they operate the coil of a N/C relay then use the relay contacts as inputs to your breakout board but it's a backward as you have introduced more things to go wrong.

Personally I would replace them all for 3 wire N/C type.