Unfortunately for your argument, the East did not ratify the Council of Florence
The Councils of Lyons and Florence did not require the Greeks to insert the Filioque into the Creed, but only to accept the Catholic doctrine of the double Procession of the Holy Ghost.
At the Council of Florence, a vigorous discussion erupted between the eastern and western bishops over words spoken by Basil claiming that the Spirit proceeded from the Father and the Son.
After much debate, the eastern delegates accepted the filioque addition to the creed (at least in the west), and made other concessions. The following quote summarizes:
“The council of Ferrara, which was transferred to Florence in 1439, witnessed protracted discussion between Greeks and Latins, in which as a final result (the primacy of the Pope) was accepted in vague terms, which seemed to preserve the rights of the Eastern patriarchs, the Greeks retained their peculiarities of worship and priestly marriage, while the disputed (filioque clause) of the creed was acknowledged by the Greeks, though with the understanding that they would not add it to the ancient symbol”.
At the Council of Florence (1439) when the Latins stated the Holy Spirit proceeds from the Father and from the Son they did not mean to exclude that the Father is the source and the principle of all divinity, that is, of the Son and the Holy Spirit.
Nor did they wish to deny that the Son learned from the Father that the Holy Spirit proceeds from the Son; nor do they hold that there are two principles or (two spirations).
They asserted that one only is the principle and one only the spiration of the Holy Spirit.
The problems on the order of terminology were resolved and the intentions clarified, to the extent that each party, the Greeks and the Latins, during the sixth session (July 6, 1439) were able to sign this common definition:
“In the name of the Holy Trinity, Father, Son and Holy Spirit, with the approval of this sacred and universal Council of Florence, we establish that this truth of faith must be believed and accepted by all Christians and thus all must profess that the Holy Spirit is eternally of (the Father and the Son), that he has his existence and his subsistent being from the Father and the Son together, and that he proceeds eternally from the one and from the other as from a single principle and from a single spiration.”
There is an additional clarification to which St. Thomas had devoted an article of the Summa (Ultrum Spiritus Sanctus Procedat a Patre Per Filium).
“We declare,” said the Council, “what the holy Doctors and Fathers stated that is, that the Holy Spirit proceeds from the Father through the Son tends to make understandable and means that the Son too, like the Father,is the cause, as the Greeks say, and the principle, as the Latins say, of the subsistence of the Holy Spirit. And since all that the Father has he has given to the Son in his generation, with the exception of being Father, this very procession of the Holy Spirit from the Son the Son himself has eternally from the Father, from whom he has been eternally generated.”
At the conclusion of the council, the reunion of the Eastern and Western Church was (joyfully proclaimed).