Current date and time:

The format is dww hmm:ss (day, week, hour, minute, second).

I cannot change the orbit around our star, so let's go with the natural 365–366 days a year. These are divided up into weeks of 7 days, making 53 weeks a year. There are 10 hours to a day, 100 minutes to an hour, and of course 100 seconds to a minute.

I propose that the 53^rd week is taken as holiday and not used to conduct any business. Note that this week contains only one day during ordinary years, or two during a leap year.

The current weekday names are poorly chosen. In English (unlike some other languages), there are two duplications: T could be Tues- or Thursday and S could be Satur- or Sunday. I renamed Saturday to Caturday ("c" as in city, obviously :-)) and Thursday to Vhursday, so that we can indicate dates in the format shown above.

In the current system, you typically specify a date like "Saturday May 7th". Or sometimes just "May 7th" and then you have to open a calendar because you are not a sauvant: you have no clue whether that day is convenient for you (you can't tell whether you work on July 7th without knowing it is a Saturday). The same problem applies to anniversaries.
Using the proposed system, you would specify a date like C11 which is Caturday in week 11. Every year.

Let's additionally specify a time: C11 400, which would be Caturday in week 11 at 4 o' clock (just past 09:30AM in the 24h*60m*60s system).

For programmers there are additional advantages to such a time: we often deal with time deltas, specified in some random format, such as seconds. What time is it 9410 seconds from now? Grab that calculator. In the proposed system, 9410 seconds from now it's almost an hour later (94 minutes and 10 seconds).
And even for normal people: tell me you never confused 50 minutes with half an hour (looking at the clock, seeing something like 15:50, and thinking it's half an hour until 16h).