My calendar problem

Today is the last day of the month.  I've been paying particular attention to this because it's the day I've been planning to announce my intention to leave Facebook to Facebook, and it starts the one-month clock during which I have to make sure I've removed all the relevant permissions and not left any documents I want to preserve on Facebook to disappear forever[1. By which I mean get saved and shared with marketing execs in a folder labeled "23 year old progressive male northeast US"]. The thing is, since it's the last day of the month, I keep thinking it's the last day of the week, too.  I've had to consistently remind myself that it's not actually Friday right now.

Obviously, the entire world timekeeping system should be rearranged to fix this error.

The Gregorian calendar is awful.  Both the starting date for counting years and the decision to divide weeks into 7 days are directly religious in nature, and even then, the Abrahamic religions can't work properly with it -- Easter, for one important date, is on a different day every year.

Better options have been proposed.  During the French revolution, a Decimal calendar was proposed, which would have divided the year into twelve months of three ten-day weeks, and five extra days, called Sanscullotides, or six, on leap years.

But the best option I've seen was one brought up on the xkcd forum:

I came across [...] the Sol calendar. [it] consists of 13 months (All of our normal months and Sol between June and July) of 28 days each and one day that's not technically in a month, which can be placed anywhere, but I like the idea of putting it as the first day of the year. The leap-year system is still employed, and Leap Day becomes December 29.

I thought the most interesting part of the system was that all of the days of the week remain the same through the entire year. I even came across one person who proposed naming the months Ace, Two, Three and so on up through Jack, Queen, and King, then naming the weeks in each month after the suits in bridge order, so as opposed to saying Tuesday, March 13, you could say Tuesday, Three of Hearts.

I'm having trouble deciding which system I like better -- the one that names the year after a deck of cards, or the one that has five days out-of-time, the way extra days should be handled, rather than tacking them onto one of the months.