Ok so I might have a logistics issue with this tree. I may be taking a new job that starts in February that is over an hour away. Would it be too risky to do the chop and root prune in February? I definitely see the soil being frozen as an issue though. How about doing it now? The tree has defoliated for winter so it’s in early stages of dormancy.
I am near Chicago, zone 5b winter - it can get pretty nasty. I don't know Long Island winters. If it were me, I would just keep it healed in the ground. If you have to move, dig, and heal in over at new place. Save heavy duty root work for after the ground thaws in spring.
You might be able to get away with serious root work and pruning now, but that is ''risky''. If you wait chances of success go up over 90%. Do it now and I don't know, maybe 60%? Hard pruning even of shrubs in the ground can cause the shrub to lose some of its winter hardiness when done in late autumn or early winter.
There are not a lot of Cornus as bonsai, some, but not widespread or common. I don't know why, whether it is a horticultural issue with Cornus being touchy about horticulture in a container? Or the fact that the medium large leaves and branch pattern don't lend themselves easily to bonsai. The photos of dogwood bonsai I have seen have been lovely.