When prepping orchard ground, there are four primary reasons to cover crop:
~ deal upfront with weed seed loading and/or rhizome grasses
~ bulk up on organic matter
~ steer biological activity in a fungal direction
~ prepare "good tilth" for digging holes
The question of scale enters in here as well. Forking out red clover root systems and then hand digging a generous-sized hole to loosen up the soil further out from the roots for a dozen trees is no big deal. Bring in a couple friends and you can do 50 trees in a morning this way. My experience with an auger was with a two-foot diameter bit in rockless ground. Soil amendments (like Azomite clay and rock phosphate) get sprinkled in and around the hole so as to be mixed throughout the soil as it gets packed back around the roots.
Another approach is to sheet mulch, and given your extensive spacing plans for trees on Bud.118, Nathaniel, I'd get right on this. Laying down cardboard would mostly smother sod root systems by next spring ... just take care to fork out grass rhizomes when surface-prepping holes for augering. Putting down mineral soil amendments at this time is a good idea, including calcium in some form.
Organic Grower Supply in Maine takes this concept to the extreme in recommending a 32# bag of "fruit tree mix" per hole. This contains worm castings, Tennessee brown phosphate, alfalfa meal, azomite, k-mag, and come form of calcium. Rich compost would be good too, all this directly on the ground (beneath the cardboard). You probably want to mow first, being it's the height of summer, to lay things flat. Atop the cardboard, anchoring it down, goes the woodsy mulch you've been gathering. Thick is good. The biological activity through the fall and even under snow cover will be prepping an even bigger hole in terms of soil friability by the time you auger early next spring. Aim to provide a minimum 4 foot diameter planting circle for each tree with this effort.
Lost Nation OrchardZone 4b in New Hampshire