There must be a misunderstanding here - either yours or mine.

Except for the A axis, you set the coordiate scheme for the nozzle check. You set the B axis and C is A cross B. This A,B,C coordinate system is your local set.

Of course, if the pipe attached to this nozzle is in X (so that A is X) and if you define B as Y, then A,B,C is X,Y,Z - a match between local and global.

If the pipe attached to the nozzle is in Y, then A is Y. You can set B to either X or Z and then C will be the remaining direction. In this case X,Y,Z is NOT A,B,C but you should be able to see your way through.

How about this? If you really must have A,B,C match X,Y,Z, put in a very short dummy pipe in X as the "anchor" connection.

If loads are magnitudes (no signs) then I don't think you have to worry about +/- X, Y, Z either.