When the going is rough, I use the tool pictured below. I picked it up at Home Depot for 16 bucks or so, and it’ll plow through just about anything. The only reason I prefer an actual digger like the Lesche is the possibility of damaging good finds. However, if your pinpointing skills are up to par, knowing where to strike is pretty easy.
I have a pick like the wooden handled one. I ran into some sun baked clay where the pick just bounced off. I took my shingling hatchet and chopped an outline of my hole and then used the hatchet to drive my old 3-in-1 knife (similar to a Hori-Hori knife)
into the ground. I had to pound it loose to get it back out. Try that with your Lesche.