Root reduction and top reduction should be done at the same time with most deciduous trees. By leaving all that top growth over a sharply reduced root system, he leaves that come out could have a difficult time. Without the root system to send them moisture, expect some wilting and die off. Tree should recover, but it could be ugly.
The "one insult at a time" thing is primarily aimed at conifers, which take more time to work. Deciduous trees, for the most part, are more immediately resilient with drastic root reduction and trunk chops.
For instance it is standard procedure here in the U.S. to chop 95 of the roots off species such as hornbeam Bald cypress, elm and others at collection and do a 90-95 percent trunk chop at the same time...