You really think short-long-short-short-long is better? It seems confusing enough to be of dubious value. Why not have seasons and months be equivalent and each equal to 73 days in length? That way you'd had the 50th day of summer, for example. Sure it would require a new season, but you reduce complexity quite a bit and there is no reason to keep the existing 12 month requirement. You can align the first month/season with the first of the year and add a 0-day for leap years.
I wanted the months to be equally-divisible into weeks of equal length. It turns out that the 7-day week is the only really good way to divide the year equally into smallish units and only have one or two days left over.
So you could have four season-months of 13 weeks (91 days) each. But I like the idea of months that are in the same ballpark as lunar cycles. Lunar cycles and solar cycles don't mesh, so you can't have months that perfectly match lunar cycles unless you're willing to have months that float against years the way weeks currently float against months, but then again some people might find that appealing.
Yeah, it's kind of fun to think about...