Without wishing to muddy the waters too much ... we need to be clear which "zero" we are talking about. The "mechanical zero" of the transducer - or the "zero" we get (take) when resetting the complete fluid system before taking an actual pressure measurement. Presumably it is the first "zero" that we are discussing here.
No chance of this value being held on the transducer itself, I suppose (followed by an element of "handshaking" between the transducer and any pod it is swapped into)?

As already mentioned, the base monitor is just that:- more or less a "dumb" monitor to display whatever is presented to it by the pod(s).
On the other hand (and forgive me for having the audacity to wonder, Dave) ... are we sure that the transducer "zero" is (or needs to be) stored at all? If you swap them about, would not the pod electronics "auto zero" the transducer each time a different one is encountered? At the end of the day, we are talking about a baseline (voltage) level - or a null reading on a bridge circuit - are we not?