The Tomus of 1285 (Finally available in English translation online, here!) Forcefully and constructively engaged Western ideas on the procession of the Holy Spirit, condemning the double procession, and the formula 'as from one source' of Lyons, but admitting an eternal manifestation of the Spirit through the Son (not merely the economical manifesation through the Son upheld by St. Photius).
Papadakis, in his scholarly exposition of the unionist controversy that lead to the issuing of the Tomus, argues that the Tomus laid the intellectual groundwork for the resolution of the Palamite controversies, which again involved interaction with Western ideas--the rationalism of Barlaam of Calabria, who was condemned by the Palamite Synods, but ended his life as a Cardinal of the Church of Rome.
The importance of the Palamite doctrine of the Uncreated Divine Energies to the praxis of monastics and to the Orthodox understanding of salvation as theosis is almost impossible to overstate. The monastic clergy were certainly among the leaders in the resistance to Florence, certainly in part because Florence in no way back-tracked on the rejection of the doctrine implicit in the welcoming of the anti-Palamite arch-heretic, Barlaam into the Church of Rome and his elevation to the rank of Cardinal.
The one hiearch who attended Florence/Ferrar, but did not accept the False Union, St. Mark of Ephesus, very much shows a keen appreciation for the Latin deviations from Holy Tradition in his Refutations of the Latin Chapters Concerning Purgatorial Fire. I see no reason to think that the lower clergy or the educated laity would have had less of an appreciation.
I believe you overestimate the ability of the Eastern laity to get their hands on Western theological tracts in 1200 and make the distinction between East and West. I think you are forgeting that there was a language barrier between East and West that shouldn't be overlooked. Did the average lay person in Slovakia speak Latin???!!! Hardly.
The Hesychast controversy is a good example of this - as no one stepped up from the East to say that the prime defender of Scholasticism, Barlaam, was not accurately explaining what Thomas Aquinas taught. Not surprisingly, the East were able to exploit Barlaam's lack of exposition and advance Gregory Palamas' ideas and concepts.
IF there were so many knowledgeable Easterners on Western theology, Scholasticism wouldn't have been so poorly represented.
Regards