You don’t. Rather, Rome accepting as valid EO doctrines is a huge step towards fixing some of their internal problems. Hesychasm and Palamist-Patristic theology could reignite the Roman church, which having throughly exhausted scholastic theology, is now wallowing in a power struggle between conservative traditionalists, many of them Dominican or members of new traditionalist orders like the ICKSP and FSSP, and left-wing Jesuit liberation theologists.
This is nonsense, to be frank; at no time in history has the Roman church claimed less authority over, or been less involved in, Eastern Christian affairs. Compare this with the 16th, 17th and 18th centuries when you had Roman missionaries actively involved in orchestrating schisms, in some cases along tribal lines* that led to the formation of the Syro-Malabar, Chaldean, Melkite and Syriac Catholic churches, to name just a few.
*Specifically, in the case of the Church of the East, the Aramaic speaking tribes in the Nineveh Plains area remained under the Church of the East, whereas the Chaldean tribe of mostly Arabic speaking Christians in Baghdad separated from the Church of the East and became the Chaldean Catholic Church.