What soil amendments should I use for the back-fill when planting the tree? None ... make the hole as deep as the root ball and 2-4x wider, drop the tree onto the bottom of the hole, remove the box, and backfill with native dirt. If you amend the soil you end up with a "bathtub" of water-retentive soil and the roots won't leave that area.

Should I use anything in the hole prior to planting the tree that will break-up the caliche like soil? Water.

When you have it dug out, fill the hole with water and let it soak in. The roots will follow the water DOWN, and are quite capable of breaking up caliche.

When you water, water wide ... spread a soaker hose along the edge and outside the planting hole, don't trickle a hose near the trunk. You want to have moist soile to attract the roots.

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We planted some Palo Breas for my DBG field work, and we used a small jackhammer to dig. Then the water truck dumped a lot of water and when it drained we planted.

No amendments, just a wide hole and a lot of water.