Manny,
Father Tom is really on the forefront of helping make TOB accessible to Eastern Catholics. He has a great way of demonstrating many of the roots of TOB in the Eastern patristic traditions, particularly in our well developed theology of icons.
As far as acceptance of the TOB, I think, as with most Catholics (Eastern or Western) it is a rather new concept (with ancient roots) as it has been formulated by JP2 and not all of its implications have been fully explored. But by and large, once it is explained, my experience is that most EC’s say “Oh yeah - that’s what we believe!”
BTW, Father Deacon Keith Fournier (he is an RC deacon with faculties in the Melkite Church) is currently completing his PhD at CUA comparing the thought of JP2 with the imminent lay Orthodox theologian, Olivier Clement through the lens of TOB. Should be an interesting read when it is done.
God bless!
In ICXC,
Gordo