You'll get better at it. Let me know when you come up with a good way to store the post hole digger. Strapping it to a tree isn't much better than hanging it from a rope.
Yes, I move the tractor back and forth when digging and also sometimes when pulling the auger up if it is deep.
Go slowly.
Oversized holes are much easier to dig and to fill than perfectly sized holes.. A bucket full of good compactable sandy clay, a shovel, a level, and a tamping rod makes it easy to backfill.
Go slowly.
Oh, and about those fancy augers with the replaceable offset digging teeth and tips - if you have rocky soil they are not only more expensive, they are worth it.
Finally, I won't have to say "go slowly" ever again after the first time you get an auger stuck.
good luck,
rScotty