When you call to get prices on the spade work, be sure to have the DIAMETER of the trunk measured. That's the important number when deciding what size spade to use.

Do not fertilize your plant, but heavy mulching and thorough, regular watering will be required. Better get it done SOON or the yaupons will struggle in the heat.

The short answer to how much root system needs to be moved with the hollies is - as much as possible. Because the trees are growing together, and reasonably close together, it may have to be a less than optimal amount that is dug and moved. Water the trees well in the days/weeks before moving them, and especially the day before - it will help the trees to be well hydrated, and it might help the sandy root balls hold together better. Water them WELL once they are in the ground.

Another consideration is getting the machinery in to dig the trees and then to move them to the new locations, although if you are having to have machinery in to put in a new septic system, then that's probably not an issue.

FWIW, I would suggest digging the new holes first, so that the Yaupons can be lifted and dropped straight away into their new homes. Save some of the soil to replace any that fell off the root ball on the voyage, and stockpile the rest to be used as needed, sine the old location will be torn up as well with the septic system installation.

I agree with Rhizo, doing it soon, mulching well - as widely as possible, no deeper than 4", and no mulch in the couple of inches next to the trunk - and watering well, for the next 2 years and maybe for 3, will dictate how well the hollies do after moving. Don't just water on a set schedule, however much easier that is, but stick a finger down into the soil and see if it is wet a few inches down. If it is, wait another day or two, and test again. If it is dry, water, slowly and deeply enough to get to the bottom of the root ball. Hot, dry, windy days will mean checking more frequently than cool, cloudy, still days.

No fertilizer is also good - the tree needs to concentrate on growing new roots for the first while, not new leaves. The only exception I would make is if a soil test shows the soil deficient in phosphorous, as that would be needed for root growth - most of the soil around here (Polk County, NC, Spartanburg C'ty and Greenville C'ty, SC) is seriously deficient in phosphates, and I always add some to the hole and back fill dirt.