I'll hazard an educated guess that there are more differences between the 22 and 23 series than the 21 and 22 series.  You can see the obvious one just by looking inside the tubs.  Your 23 has the Whirlpool Power Clean module, which looks nothing like the Hobart-designed assembly on series 22 and older.

Whirlpool's influence was far more pronounced beginning with the 23 series, so I'd wager that the electronics from the 22 may not be an exact match.

If any of the KA experts reply to this thread, they'll be able to provide details.

The Imperial (KUDI23) parts you mentioned would match. 

Whirlpool did make improvements to the electronics, but the 23 series may have preceded them.  Hobart's electronics were notoriously failure-prone.  If someone here can confirm whether the 23 series used the improved version, that would help you decide if sticking with 23 series for back-up is the best, if not only, plan for you.