Enh, the 'root pruning' Ann describes is traditionally recommended but I have seen a number of recent sources questioning its wisdom, on the theory that it may be better for the tree to have to regrow its roots only once rather than *twice*, which frankly seems pretty reasonable to me. I am not aware of any controlled studies directly comparing the two methods, but from a theory standpoint I would personally skip the root pruning (although it
would be appropriate for something like separating a natural offset from a shrub). IF you *do* decide to root prune, it should be done at least a full growing season before you move the tree (to allow good regrowth of roots), which I'm not sure how practical that would be for you.
But as Ann says, the trees should still be transplantable -- just. You need to move them when they are NOT in leaf. Whether to move them now depends on your local climate -- is your soil currently suitable for root growth (and will it continue to be for the next month or so)? If not then I would wait til its earliest workability in Spring and move them then (asap!).
Alas you will not be able to move a 4' diameter root ball - not even with two people. It is still worth making your 'digging circle' that far out, but realize that you will then have to carefully excavate your way back in towards the plant with a trowel, preserving the largest roots or groups of roots, til you get a more manageable size rootball.
Do not try to lift the tree onto a tarp -- lifting it by the trunk with the heavy weight of the soil hanging off its roots can cause severe damage to the roots. Whatcha wanna do is rock the tree to one side as far as possible (once you've got its rootball all sorted out and completely separated from the surrounding dirt), slip a folded strong tarp as far underneath it as you can reach, then tip it the other way (now the rootball will tip onto the tarp) til you can unfold the tarp so it's now entirely under the root ball. Lift the tree out of the hole BY THE TARP, and transport it that way.
Have the hole it's going into already dug and prepared so the tree doesn't need to sit with its roots waving in the air for more than a couple minutes. Before you plant it (as per Ann's directions) scratch a cup or several of bone meal into the soil at the bottom of the hole - no other fertilizer or amendment, just bone meal. If the location is windy, do make SURE to stake the tree, just make sure (as described) that there is a little slack in the ropes so the tree can sway naturally with the breeze to strengthen its roots and trunk.
With trees this size, the aftercare will make or break the move, and the trees will need coddling (not overwatering, but coddling nonetheless) for at LEAST the whole next year.
And btw, speaking from personal experience here

if the trees are being dug up from right alongside the house, I suggest you find some replacement soil and stomp it in REALLY HARD into the holes they came from, preferably crowned higher than the surrounding soil, or you may have some exciting wet basement problems after summer storms
Jealous that you can grow redbud in your climate

,
Pat