Thanks for the Date Code conversion calculator. It helped me out so I would like to return the favor.
In your note you said you couldn't find a mathematical way to determine the first Saturday of July, so I came up with one for you (see below). Basically it starts with the 1st of July and then adds as many days as necessary to move it to the first Saturday. If July 1 is a Saturday, it adds 0 days.
July1st = July 1, YY-1
1stSatInJuly = July1st + Mod(7 - Mod(July1st, 7), 7)
Mod(7 - Mod(July1st, 7), 7)
0, 6, 5, 4, 3, 2, 1 for Sat, Sun, Mon, Tue, Wed, Thu, Fri respectively