They make a tool that fills these holes. Its called the Lynsky tree feeder. It costs like 350 bucks! Actually the hand method isn't all that bad. You have to push the hole down anyhow to make sure its filled so its not all that redundant.
As far as the backfill mix, I use a granular compound that consists of various ground meals, kelp, worm castings and humates. I have top dressed sites as well as a more basic and cheaper form of soil amending. Vertical mulching gets the material where it needs to be on mass and quicker. I don't do that much radial trenching as it is cost prohibitive and time consuming. Im not against using it but haven't had too many customers want to spend the extra dough to make it happen. Generally we will soil drench or root feed these sites twice annual with compost teas/liquid humates after the process.
Jamin, chicken poop is one of the most common additives in most granular organic fertilizers.