Well. That depends how you measure it. You get a different answer depending on whether you’re measuring the mean tropical year, or spring equinox to spring equinox, or winter solstice to winter solstice, or etc.
Also your descendants will get a different answer when they measure it in a few thousand years time. If this calendar was adopted, it would get abandoned before a 60k-ish year cycle completed and a year with three leap months was inserted, let alone a year with four leap months. It feels like bugs would slip in.
Better would be to adjust the cycle so that leap years occur slightly more often, but no more than one month is added to any one year, similar to the proposal that 8 years out of every 33 in the Christian calendar should be leap.
If you just made Christmas into such a day or added a festival day it would help make the day special and make ordinary years line up, in the case of leap years you would have to add another “day out of time.”
I think though that a lot of organizations would struggle to fit a day like that into their scheduling systems, though in the case of Christmas almost everything shuts down anyway.
See
https://www.crystalinks.com/dayoutoftime.html
for the version of it in the calendar I mentioned.
They do this for profitability, as it allows them one additional billing cycle per annum. I feel it's dishonest, they feel it's "business as usual."
[1] https://en.wikipedia.org/wiki/International_Fixed_Calendar