The support blocks and mounting plate method can be as shallow or deep as you like -- as long as you leave enough so you can't pull the stick through it during vigorous play.
Scott

I mention that because if you need to mount it that shallow, you should change to a top mount approach.
Personally, I try to avoid top mounting sticks since it makes it harder to repair/service/replace, but with some sticks, you can't avoid it.
So leave a minimum or maximum 1/2 inch from the top? Sorry for the dumb question. Also do I need to drill all the way through the CP or just .4" from the back for the GGG thread inserts?
ABSOLUTE Minimum -- ANY closer than that and the mounting screws will probably punch through the top. Leave yourself some wiggle room.
You will want to drill the holes for the inserts deep enough that the mounting screws don't bottom out and push the wood up so it deforms the CP surface, but no need to drill all the way through.
I went a little shallow once and had to carefully drill through the installed inserts so the screws could tighten on a Zippyy.

You can't remove the inserts and reinstall them in the same hole -- guaranteed fail.
The best approach is to get the inserts and take careful measurements
before you route out the joystick recess.
You can mount the stick on a piece of scrap MDF if you want to practice before you do it on your CP.
The good news is that you can carefully remove the GGG inserts and reuse them, just not in the same place.
Scott