Weeks should have ten day weeks

And instead of calling them “weeks”, we could call them by the much more self-explanatory term “tendays”.

summer/winter solstice and the spring/autumn equinox as well as new years day are special holidays that fall between months and interrupt the week cycle

You can simplify it a little bit by putting the intercalary days between months, rather than using them for the solstices. We can put Midwinter between January 30 and February 1 and Midsummer between July 30 and August 1, in the northern hemisphere.

For the sake of putting it in a more user-friendly location, our leap day should be in the summer for the northern hemisphere (where most of the population is). So put it the day after Midsummer.

The only thing I would do differently from the Calendar of Harptos is that, like you, I would use New Year’s Day as the 5th annual intercalary day.