Store the actual Z-axis limit or an offset by pressing a button on the PanelDue.
Do you mean store it on the SD card so that the Z=0 position will be the same after a power cycle? If so then the only way I can think of to do this now is:
To find the new Z=0 level, after placing the nozzle 5mm above bed centre, send G30 with the Z probe type set to 0 (P0 in your M558 command).
Then send G1 S3 Zxxx Fyyy (with appropriate xxx and yyy values) to send the head or bed ot the Z-max endstop. When the endstop is triggered, it will adjust the M208 Z limit. Then send M500 to save the new value in config-override.g.
The M586 command followed by M500 almost does what you want, however there is currently no facility to use M586 to probe manually instead of using a switch.