I have been digging up numerous small trees in the last couple of years with my loader and no tooth bar. Here is what works the fastest for me to get a deep, but not long hole.
1. Curl the bucket way down - not vertical, but definitely down there.
2. Use your joystick to push the loader down into the ground hard. Let the front wheels lift up a little, so you know you have some down-pressure on it.
3. Start curling the bucket upward.
4. When the bucket has curled a little, give another downward push into the ground with the joystick.
5. Keep alternating between 3 and 4 until the bucket is fully curled upward. At the same time, keep trying to move the tractor forward to keep forward pressure on the bucket. It doesn't take long to get the hang of this.
It's true that with the front wheels off the ground you don't have as much traction, but this method doesn't rely much on traction. Of course, you will still end up with a five foot wide hole for a two foot wide root ball, but without a backhoe, what else can you do?
Tom