Collecting oaks in California is not the same as collecting oaks in Fla. Eastern oak species can be a bit finicky when it comes to root disturbance--even live oaks. Sever the roots all at one go and the tree will probably die.
A more conservative approach is needed, in most cases here. All this depends on what kind of oak you're digging. Willow oak can be dug more aggressively than tyipcal White Oak and red oak, for instance, since Willow Oak (Quercus Phellos) has a shallower root mass than most other oaks. Live oaks in the east (Quercus Virginiana) are considered white oak species
The biggest issue with white oak species in the east is tap roots. Tap roots can be quite significant if the tree is over 4 inches in diameter. If you cut it all at once, the tree may not make it.
I'd trench the oak in early Feb in your part of the country--just before bud break. Cut through the larger roots at the surface all the way around. Make sure you undercut half the root mass to incorporate the tap--which should be cut half way through. Backfill with bonsai soil. Let it alone for the year. Repeat the process from the other side the following spring.
All this is rather subjective and depends on the tree and local growing conditions. The best thing to do is experiment a bit with a few trees that aren't that terrific bonsai-wise to get experience in how to do it. I'd not dig all 20 of those trees all at once. Try three or four to start. See how you do.