There is actually a good amount of material out there by Eastern Catholics, so long as you know where to look.
Anything by (Melkite) Archbishop Joseph Raya is AMAZING and worth reading. I know of a good number of Eastern Catholics turned Orthodox who still gain a great deal of insight from reading the writings of Archbishop Raya.
The writings of Russian Catholic (turned Orthodox pretty much on his deathbed) Jesuit priest, Fr. George Maloney S.J., are also very good and very much worth reading.
Irenee Hauser, as mentioned in an above post, is also a worthy read.
“A Monk of the Eastern Church,” aka Archimandrite Lev Gillet, is also worth reading. It is noteworthy that he turned Orthodox long before his death, but never considered his translation into Orthodoxy as a rejection of Catholicism. In fact, he remained close friends with a number of Eastern Catholic hierarchs throughout the remainder of his life - including Met. Andrew Sheptytsky.
The Venerable Catherine Doherty is also a good read, although her works do tend to be somewhat Latinized (not too badly though).
Melkite Bishop Nicholas Samra also has a few works out that are definitely worth reading, as does the late Melkite Archbishops Joseph Tawil and Elias Zoghby.
Ruthenian priest Fr. Jack Custer has also written a number of books on the Scriptures from a Byzantine perspective. They are very Eastern and definitely worth reading.
Finally I would recommend the writings of Roman Catholic scholar, Fr. Tomas Spidlik, who was claimed by the Romanian Orthodox as “one of their own” for his extensive work in the area of Eastern Christian spirituality.
That should be a good place to start with both Catholic and Orthodox writings on the East.
I would recommend avoiding anything by Adrien Fortesque. From what I understand he didn’t think to highly of the East (Catholic or Orthodox).