The only trick to transplanting orchard trees is to make sure you get enough of the root system balled up and then plant in a hole that is 2x the size of that root ball side to side and only as deep as the root ball.
Most failures I've ever seen were because they didn't take enough of a root ball, there is a fairly easy way to calculate how big the ball needs to be.
Diameter of the trunk in inches x 6 = distance from trunk to cut line for root ball, to be really safe you can use D x 10 = distance from trunk to cut line for root ball.
Note: the root ball depth needs to be the same as trunk to cut line measurement to be sure you have enough of the structural roots (main branches).
Thank you Dr RedHawk. I’m very curious on the looks and condition of the rootball. Would you recommend any amendments by chance? I’m going to be testing the soil of the new site to A/B where the apples are at now.
Don't wait too long. You'll want to pull them from the ground while they are still dormant. You can always put them into a pot even if you're not ready to transplant them to their new location.
And you'll probably want to cut back the branches about 40% or so, to assure that the root to shoot ratio is balanced. If you leave too many branches, it will stress the tree tremendously as it tries to feed all the new leaves that will emerge.
"The rule of no realm is mine. But all worthy things that are in peril as the world now stands, these are my care. And for my part, I shall not wholly fail in my task if anything that passes through this night can still grow fairer or bear fruit and flower again in days to come. For I too am a steward. Did you not know?" Gandolf
The trees should do fine in the native soil, I am not a proponent of the amend the soil back fill. It has been shown that doing that, giving access to better conditions in the planting hole, tends to act like a container, meaning that the new roots will tend to circle inside that hole with the amended soil and not get out side that hole diameter. What we want is for the roots to expand away from the trunk and form the stabilizing spread of a trees natural root growth.
Marco filled in the blanks that I didn't address in my first post (thank you Marco, that was awesome info for the OP).