I don't think the proofs for the existence of God are heterodox, though perhaps considered unnecessary or unwanted by some Orthodox. Here's a quote:
"The so-called logical evidence for the existence of God is: the cosmological, theological, psychological, historical, ethical proofs, and many more, which, through the passing of time have been formulated into philosophical rationalism. They cannot, in the Dogmatics of the Orthodox Church, have a value of real evidence because they are based on the principles of the relative, limited, sinful minds and senses of humanity. To the Church and the Revelation, the truth about the existence of God is an illogical and irrational hypothesis, which has the need of proof with the basis of logical reasoning, the truth which God has revealed to us, and is therefore the unquestionable, true evidence. As a divine and given reality, this truth is not dependent on proof and arguments from rational functions of the mind. The logical proof proves God so much more than it hides him." - Justin Popovich, Orthodox Faith and Life in Christ, p. 202
Fwiw, if you haven't seen it yet, there was a thread on Aquinas
last year that you might find interesting. Sorry that I can't add more, I've never read that work by him.