I assume the right way to deal with this is to have a name for each set of calander rules, and convert dates into and out of them.

Not labelling the calander your date is from is more understandable than timezones, even if most calanders have confusing names for months.

Thankfully, it's the month of 'Sol' in the IFC system right now, so no confusion. (Messidor in the French Republic calander)