Of course this goes without saying, but I'd like to mention it anyway:
Though the variability of weather and temperature at any particular time of year is greater than the astronomical inaccuracy of Nearest-Monday, people could nonetheless prefer maximal astronomical accuracy over maximal convenience.
...in which case they'd prefer and choose a non-fixed calendar.
For my 3 proposed alternative calendars, or any calendar, that would just mean
substituting the words "The midnight nearest to the intended-time" for "The Monday that starts on the midnight nearest to the intended-time".
That could be called "Nearest-Day", or "Nearest-Midnight" as opposed to "Nearest Monday".