As stated above, this has been discussed to death here. You really should click on the tags below and examine some of those threads. Some of the threads lead to the private forum, so if you are not a member of the private forum, you may want to pm an administrator for admission.
In a nutshell, the OO's would highly contest your assertion that St. Cyril would be O.K. with Chalcedon. These are a few of the reasons given in past threads:
1. In the agreement signed with John of Antioch, St. Cyril agreed to language to the effect that Christ was OF two natures. Chalcedon said IN two natures. There are theological implications that go with that language.
2. St. Cyril wrote On the Unity of Christ after the above agreement. In that book, he upheld "one nature" as more proper.
3. Since St. Cyril died before Pope Leo's Tome was written, we can't know for sure if he would have liked it. However, we do know that Nestorius lived long enough to read the Tome and approve of it.
4. There was language in the Tome which attributed different actions of Christ to one nature or another. St. Cyril explicitely condemned this practice in his above mentioned book.
5. Chalcedon was initially accepted by some groups that were explicitely Nestorian, such as the Nestorian Persian Church.
So on and so forth, blah, blah, blah...
This has all been discussed to death here in the past five years, both in the private and public forums. The EO's have presented cogent and well-crafted resposes to all of the above points, as well as other points we OO's like to make.
This all reached a boiling point in June of 2004, here in the OO section, with some extremely contentious threads. Two members-one of whom I respect highly-left OC.net over the issue, and over time the private forum was created to take discussions about Chalcedon that wax polemical.
You are not going to find too many people here wanting to discuss this again, as the subject has already been beaten to death repeatedly. As it is, if this thread goes much further into the discussion, I'll probably have to move this to private. Thus the advice to look at past threads, and if there is something about Chalcedon that is not addressed in all those threads, post that question. You may want to do it in the private forum, though.