Question
Dug a 12" hole about 24" in diameter, also dug a 6" hole 24" in diameter.  filled both with water at 5:00pm yesterday.  The 12" hole went down about 2" and the 6" hole went down about 1".  it this a problem.  let me guess - yeah.

Answer
Yep! That is a big problen.
Dig as far down as you can, and mix the soil you take out with te mixture I gave you. BUT, instead of 1 part clay soil and 1 part mixture, I would put 1 part soil to 2 parts mixture. you have some serious clay there.
Dump that gypsun on top of the area you dig out, and them replace the soil with the good stuff you have mixed up.
Know what, wouldn't hurt to mix some of the gypsum in with the clay and mixture. It would just get more gypsum seeping into that hard clay at the bottom.
If you have 10 to 12 inches of good soil, that should sustain your grass, while the gypsum losen up further down over the next few years.
8 inches of good loose soil would sustain a nice lawn, the problem is, the water just goes down to that clay and stays there.
Charlotte
PS. Know what you might consider?
There are some really neat ground covers that are more shallow rooted, and like wet feet, so they would fare better in that soil, until, it has a couple of years to loosen up. Some of them are evergreen, some of them have delicate little blooms. some grow 8 to 10 inches high, some only grow 4 to 6 inches high. you can maow them if they get higher than you want.
There used to ne a very few ground covers that would grow in sun or shade, now there is a whole slew of them.
Some have broader leaves, some have tiny leaves.
You just might like them really well.
8 inches of los soil shopuld sustain most of these ground covers. Meanwhile that gupsum would be working.
If you want more information about thise ground covers, let me jnow and i will send you some sites with them, so you can check tham out.