13-month Calendar

Yay, another calendar post. I've found a lot of information on 445 and all that, but not the 13m/52w/364d ones.

So far, I've built my query so it loads up a calendar which continues from 2016 and covered things like start of week conditions, fiscal year conditions, etc. But getting day of week, week of year, and period (month) of year is very tough because of the conditions of a 13 period calendar. 

Here they are:

1. Weekday starts Monday
2. Fiscal Year starts July
3. Fiscal year start is ISO meaning the starting week of fiscal year is when 1st July occurs on Mon-Thu. I.e. if 1st July is a Friday, the year will start the following Monday, 4th of July.
4. Because the year is 364, some years will have a period that is 5-weeks in length at the start (or end) which prevents falling short

Any ideas?