How can we reconcile Al-Tahawi's statement: "We do not expel a servant from faith except by denying that which admitted him into it," with the Hanafis' extensive pronouncements in their fiqh books regarding excommunication due to actions? And what are the foundational principles of these pronouncements, and what books are beneficial in this matter?

Al-Tahawi is not obliged to agree with the later Hanafis; he has his own choices. The Hanafis themselves differ on the sub-issue of whether intentionally praying without purification constitutes disbelief or not. Those among them who deem it disbelief justify it by contempt (istikhfaf), which is akin to denial (juhud). In this matter, it is the contempt that necessitates deeming one a disbeliever, not the abandonment of the obligation itself.