The twice the root ball size for the hole is a crock. The hole needs to be big enough so that you have room to pack around it without leaving air pockets. I figure on 4" ring around the tree. The tree is going to have to learn how to live with clay at some point, so use a mix of local soil and potting soil for the transition.
The single day rental on the loader is suspect. If you are doing two trips with the dump truck, you are going to need the loader just for them at the destination site. You have to auger the holes, but you don't want to swap back and forth between the auger and the bucket (or forks) for moving the trees.
You may end up renting the loader for 2 days.
We have an outfit here that will rent, and you can pick the unit up near closing time the night before, and return it the morning the day after, and still pay for 1 day's rent. If you have the right people, you can have one member work during the evening and get your holes in. The next day, you can move to a bucket, and move a tree by each hole. As the crew finishes each tree, you can pick up the grunge, and deliver mulch for the next tree.
What size root ball are you talking about. Up to about a #20 pot you won't need the loader to plant the tree. Certainly you *will* want it if it's a #35 for #50 pot.
For what it's worth: I recently did a job with #10 growbag birch. The holes were pre-dug. Stripping the bag and planting the tree: 6/hour. Pulling excess soil into heaps away from the tree, ready for pickup. 12/hour. Weed barrier and mulch. 15 per hour. Net: ~3 trees per hour. Working solo. Would have wanted a partner working with larger trees. Even a #10 bag with field soil is about 80 lbs.