What, 2023-223 for the 223rd day of the year 2023? That... is oddly appealing for telling the actual progress of the year or grouping. No silly "does this group have 31, 30, 29 or 28 members", particularly the "is this year a multiple of four, but not of 100, unless it's also a multiple of 400?" bit with leap days.

You'll have oddities still, no matter which way you slice it, because our orbit is mathematically imperfect, but it's a start.