My ideal is dropping the month altogether for 13 week Quarters with the last day being an intercalary outside the week and same for leap days.
If you wanna avoid huge date numbers, break it down further by weeks, so for example my BDay this year would be 3.10.3, third day of the tenth week of the third quarter.
As for year counting, I like Era of History for the current era, dating to the invention of writing, Era of Legend, dating back 100k years to the earliest date that stories we have preserved now would have to date back to, Era of Evolution, which dates back to the development of Life on Earth, Era of Stars which dates back to the birth of the first Stars in the Universe, and finally the Era of Energy, in which the universe was so superheated that large cosmic structures were physically impossible, dating to the Big Bang.