In my experience, if you are in very hard ground, you may want to investigate using a more aggressive digging tip for your auger, something more akin to a rock bit.
I did some holes for a neighbour a couple of years ago in hardpan with rocks, brutal digging conditions. The auger was very hot each time I pulled it out of the hole, and it wore the chizels down pretty good.
If you have the option, do the digging when the soil is wet, like in the spring. This too will help a lot.
As stated earlier, you will have no problem running an auger with your machine. I am running up to a 12" auger on an old 440B with acceptable results.
HTH