Might try a different auger style. Some have higher density spirals than others. I use a 12" open spiral auger. The open spiral has a steeper blade pitch to it, causing it to pull itself into the hole. Maybe I'm lucky, but haven't gotten stuck nor had trouble drilling yet. Have gone right through 5" roots without so much as a grunt. Soil here is all clay too. I did do all my drilling in the spring when the ground was pretty wet though.
Both my augers have different "pitch on the threads" starting just above the replaceable tip and going up nearly a foot and then go courser the rest of the way up.
I have drilled dozens and dozens of holes when there was fair soil moisture. I suspect our drought is the culprit. Even though we got some rain the soil is only moistened a couple inches down from the surface which is how far I can "drill" before just spinning uselessly. If I invested a few hours every day for a week or so just running around making sure all the little shallow holes I can dig were full of water I might get the water to soak in deep enough to be able to make the 3 foot holes I want.
Egon, I have a length of 1/2 inch galvanized pipe about 5 feet long with one end cut like a hypo needle and a T fitting on the other. I have an adapter on the side of the T (horizontal port when the pipe is vertical) to accept a garden hose. In use I pound it into the ground a bit, turn on the water and either push manually or hammer it down into the ground. The hydraulic mining action usually blows a hole fairly easily. I have used it to tunnel under sidewalks or to probe into the ground looking for a buried structure, or...
The pressure washer idea you mentioned would be like my home brew rig on steroids! Around these parts finding the fittings needed to set up a rig based on a pressure washer might be difficult but there is always tele-buying via the web. (I really prefer seeing the stuff in my hand when boldly going where I have never gone before.) Except in summer, when you might not mind hosing yourself off, my rig has the downside of a guaranteed mud bath. I have good rain gear but a wet suit (with face mask would be better sometimes.
Since I have had several good years out of the PHD and only have trouble with hard ground, I should probably not be so concerned with an equipment change as exercising patience and spending time watering the little dimples I CAN MAKE to soften the ground.
One of the holes I dug was a dream, just went like a textbook example. This was on a gently sloping area, not a depression, and gave no evidence as to why the soil should have been damp all the way past 3 feet down. Of course I have no clue as to all the varioius subterranean paths of water flow. I have a location near a hilltop that stays muddy (and may show surface water) when all around it is dry.
First I have to repair or replace the PHD then start toting water. It will be light enough to see good enough in a few minutes so I will start my exploratory surgery.
Thanks, everyone for your comments. It helps me organize my thoughts and of course supplies ideas that might never occur to me.
Pat