Honestly, I'm still attempting to digest and formulate just how his work helped me to become Christian/Orthodox, but I know that it greatly influenced me.
For some reason, his writings were the first Christian ones to ever resonate with me on a personal level. Confessions, City of God Against the Pagans, Milton, Dante, Thomistic stuff, etc. were fascinating, but they didn't challenge how I lived or what I believed. I had a noticeable aversion to the boiled down message contained in Mere Christianity, which led me to acknowledge that there might be a certain truth behind it.
I understand your (Orthonorm's) view on Mere Christianity, but I think it somewhat misses the point. He didn't intend to write an exhaustive or definitive theological work capable of standing up to scrutiny. Rather, he just explained how Christianity finally made sense to him: an intelligent, skeptical, highly educated atheist. Presenting this work as a series of radio talks to a war torn Britain of waning faith underlines its actual purpose. You're right that it shouldn't be put forth as an exemplary apologetic, but some of the simplicity was what made it compelling to me. Ultimately, I'm not sure Christianity is meant to be able to stand up to forms of critical analysis, but that's a different topic (and I always welcome reading suggestions). I think that's what Thomism attempted and failed to do.
Also in defense, Mere Christianity is a great primer (if one is needed) for The Screwtape Letters.
The Great Divorce stuck with me as well. I don't want to overemphasize the similarities, but I think the concept presented was somewhat compatible with certain Orthodox perspectives.
Another way in which Lewis' work helped guide me into the Orthodox faith was through his illumination of Spiritual Warfare in modern, applicable settings. The conflict described in The Screwtape Letters and the one detailed in St. John of the Ladder's great work, particularly within sections of the 15th Step, strongly resemble each other. Again, I somehow recognized these works as truthfully representing our struggle.
Alas, I'm unable to accurately determine the level in which C.S. Lewis' writings helped, and how much the Holy Spirit prepared me to receive the message of Christianity and Orthodoxy through his and other authors' work.