I also don´t think that we can classify him as a Thomist in the strict sense of the word, despite his strong connection to the Roman School. Some people even call him a "Hegel of Catholic theology", saying that he created a kind of theological late-Idealism or romanticist theology.
My impression of Rev. Fr. Scheeben is that he was to the study of Sacred Theology what Msgr. Knox was to the study of the Sacred Vulgate amongst the Anglophones: very beautifully and refreshingly coalescent, but with a certain unnerving novelty that necessitates a very thorough familiarity with the Douay-Rhemish translations in order to estimate its merit. So likewise, Rev. Fr. Scheeben ought not to be read without a previous solid foundation on Thomistic theology and philosophy.
He has been abused much by the theologians of the "Vatican II" era, who read him without a strong Thomistic foundation, or who sought him out as an alternative to the Thomism they sought to undermine.
He is also very difficult in his language, making his writings on the mysteries sometimes quite mysterious!
I love his language, though I have to read a sentence fives times on three non-consecutive occasions for me to fully comprehend the meaning thereof. His style embodies an Eleusinian sublimity that is as lovely and haunting as it is intimidating.
His notion of "super-nature" is truly ineffable.
What is largely unknown is his theory on the "self-termination of the teaching authority" through heresy. Only one or two sedevacantist authors picked that up - maybe also due to the fact that his writings are no longer very much known outside of the German speaking countries.
Oh, I'd like to know more about that when you have the opportunity to discuss it.