Here's what I've done: First, I transplanted 10 root shoots from a purple locust, honey locust, and cottonwood poplar. I dug up the small shoots and as much root as I could. I moved them into holes with a 2.5 foot diameter about 1 foot deep. I filled the wholes with good organic compost from my horses. I watered the plants with a B vitamin complex meant to reduce transplant shock. It's been a week and a half. The transplants are all still green but drooping and none look promising. But I am going to keep caring for them and see what happens. I would like to try this method on rocky mountain or silver maples as well as Russian olive. All of the trees planted into the ground like this will stay here when we move - again, I am learning.

The second thing I have done is taken cuttings. As a newbie it is very hard for me to know on some types of trees if I am taking last years wood or the new stuff from this year. So, to be safe I did not plant anything longer then 6 inches from the tip of the branch. I removed most leaves and all seeds or flowers and injured the trees by gentle scraping off the bottom half inch of bark. I then dipped at least 2 nodes into rooting powder (Rootone) and planted the cutting into a peat moss 3 inch planter (the kind you plant directly into the new location because the roots eventually grow through the cup) into an all purpose grow mulch/soil mixture (I chose this mixture because I do not know if the compost from my horses is high enough in Ph or what to include in a mixture I create myself so I chose something that boasts to be intended for my purposes). I have a variety of purple locust, honey locust, cottonwood poplar, fruitless pear (upright, not weeping), russian olive, silver maple and rocky mountain maple and finally a red wood and red leaved small tree variety I have not identified yet. I will do some weeping willow, blue spruce, and quaking aspen soon as well. I have planted way more cuttings then I actually want to plant when we move. But I am compensating for a margin of error - I know they won't all make it! Finally, I have the pots in the shade outside and I water them 4 times a day with a light spray until the pots are thoroughly wet. These have all only been potted a few days so I do not have an update worthy of note yet. They are all standing and green except for the red leaved variety which looks very limp in almost all the pots- but that's it.

Please pick apart my process. Tell me what I am doing right and what I am doing wrong - also, what else you might recommend.

As for your transplanting, it is not recommended that you fill the planting hole with anything but the surrounding native soil...no compost, etc. The holes should be dug only as deep as required for the root ball to sit at or a little above the existing grade, never buried with new soil.
The holes should be more like a very wide basin, rather than a hole.

Transplanting will be more successful if done in the dormant season or in early spring before new growth commences.