I don't think that this is feasible. Too much of the date stuff is hardcoded.

There are some things which you can change in various ways, but it will be difficult for your players if some parts of the UI use one calendar and other parts use a different calendar.

The date which is displayed in the top-right corner is set up in interface/speed_controls.gui as:
But what is displayed there is created by eu4.exe in some way, but eu4 does not allow code mods which could change the code in eu4.exe.

But you can probably use a scripted UI to put some other text box above the normal DateText and/or move the DateText to a position outside of the screen. You can probably somehow calculated the date which you want and store it in some kind of variable which you can show in that scripted UI. But that won't change dates in other places of the UI. Some places which show a date in a specific text box could be changed in similar ways.

But dates in tooltips are problematic. You can change some of the date formatting with the following localisation strings(LONG_EU3_DATE_STRING is definitely used in some tooltips), but I don't think that it affects the date on the top right of the screen:
Maybe one of them supports customizable localisations and can be changed dynamically, but I doubt that.

I would suggest making a scripted gui below (where the points are displayed) to show the alternative year. That way players can see both and won’t be confused by potential triggers or effects (that would print the actual game year).