I have transplanted lots of Magnolia stellata.
Dunno about your specific cultivar... but...
I'd be tempted to just propagate by layering... cover the end of a limb with soil... roots very easily.
Then move the rooted pieces.... this way, I'd have the children in places that I thought they might do better while not endangering the original.
If you are determined to move the original tree... I would wait for the temp to break and the autumn rains to come... and then move the tree.
In my area... probably next month.
