If you are digging 1 ½ feet, and are reaching water,, Here is my suggestion. Dig down as deep as needed to steady your posts. Yes there will be water in that hole, as you are removing the soil. So lets assume you reached your desired depth. 2 feet,,,,, 3 feet

Take your post, and treat the earth depth portion with roofing tar. (brush it on or dip into bucket and brush up.)
Treated lumber is not as good as it used to be before. It still is green tinted, but not very resistant to rot as previously. Mostly just resistant to insect damage.
Try to remove most of the water out of the hole. Drop some dry concrete mix into bottom of hole. Then set your post on top of that layer. Then Position your post straight and plumb, and secure into place with whatever bracing works for you. Fill the hole with dry concrete mix to
just above the water line level. Pound down tightly all around your post. (meaning pack the dry concrete mix tight.) The water will wet the concrete on its own. Next day, fill to top with wet concrete, and you have a well set post.
I am wondering why you are using 6 x 6 lumber. It seems an Overkill. Of course I don't know exactly what your plans are.
Ask anything else you are not sure of. I tried to explain as well as possible, but sometimes things do need some further explanation.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,and