" Well, by that logic, "zontos" is a participle working as a an adjective, and it is not inflected"
You know, you're right, but it modifies pillar, does it not? The real question is what does the entire clause modify.
Off to court!
"Zontos" modifies "theou", by common sense, and yes, it is therefore ungrammatical no matter how you look at it. Unless we subvert all translations known to man, and translate, grammatically
"the God's Church, living, pillar and foundation of truth".
I think it is a colloquialism that is in too much of a hurry to separate subordinate clauses with prepositions.
"ekklesia theou [pas o] zontos [e de] stylos kai edraioma tes aletheias"
Or any combination.
The point remains, God is no architectual support element of anything, but the Church, metaphorically is.