Hey, I quite like this! You're the first person I've found that's thought of fixing the calendar by adopting six-day weeks. I have a very similar personal version, with two main differences:

• there's a leap week instead of a leap day, that way weekdays are always the same without having to skip any and every year has a whole number of weeks (either 61 most years [roughly 7 out of every 8] or 60 on short years [roughly 1 out of every 8])
• December includes this leap week and it's either 30 or 36 days long, depending on the year. I put it at the end of December for the same logic that you put Saturnalia at the end of the year, to not mess with cardinal dates and so that the Xth day of the year is always the same date

I also came to the same conclusion about workweeks. With two-day weekends, the Gregorian calendar has 71 % of workdays but the new calendar only has 67 %. On a thirty-day month this means 20 workdays instead of 21,5. Having the six-day week could also theoretically allow for a move to three- or two-day weeks in a post-scarcity future and doing away with weekends, as well has having either 50 % or 67 % of the workforce being active every day of the week, and not the wild levels of fluctuation seen today. Not having 100 % commuting some days of the week and a fraction of that on others would allow to scale things like transport infrastructure much more effectively