Use G52, this seems to be a perfect application; G52 is a command that sets a secondary work zero with reference to your main work zero.
What you need is some way to locate your main work zero; you have the hole that you probe so make this your main work zero, call it Gmmm.
You know the distance(s) from this hole to your intended G110 and G111 locations and these are used in the G52 command:
Gmmm G52 X(distance110) Y(distance110) Z(distance110)
This command uses the Gmmm as a reference point and establishes the G52 secondary work at the point you want your G110.
The machine will continue to use this secondary work zero until you change either Gmmm or give a new G52 command.
To get to your G111 location all you need is another G52 command using the 'distance111' and a main work zero placed at the bottom hole.
Same for the other faces.
Actually if you make your main work zero in the center exactly between the two reference holes you can do it very easily. We have numerous rotating fixtures that consist of a base with a central hole that is used to locate a main work zero; anything up to 32 secondary work zeroes are then referenced from this using G52.
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