I bet esshup can be some help with that. He'll be out of pocket for the next day or two, but IIRC he's dealt with the exact same thing.
I'm back!!!!!!!!!!!!! Roughly 1800 miles in 2 days.

Posts have to be set below the frost line, which is usually around 38" here in Northern Indiana.
Dig a 4' deep hole, making it wider on the bottom than on the top. Like an upside down mushroom if possible. Drill some holes thru the posts (if wood) and place rebar thru the holes, sticking out from the posts 2"-3" on each side. Go buy the fast set post hole bags of cement from your local box store. That type needs no water to set up, the ground water will be enough, or you can pour water on top of the cement after you pour it dry into the hole.
Anyway.........
Pour 2"-4" of cement in the hole. Set the post on top of that. Brace the post so that it is vertical and facing the way you want it, and then fill in the hole with dry cement right from the bag. 24 hr later go back and remove the bracing.
Here's the cement that I'm talking about.
Fast set cement The key to stop the heaving up out of the ground is to have the bottom of the cement larger than the top. It acts as an anchor against coming up.