Actually, the leading theory is that "(W)ilios" was the Hittite "Wilusa". Indeed, there are Hittite texts that talk about "Wilusa" (Illios), "Alaksandu" (Alexander), "Appaliunas" (Apollo), Taruisa (Troia or Troy), and war with the "Ahhiyawa" (Achaeans). Your interpretation and certainty is not mainstream, which is why I would like to look at the sources. Just saying that this is so doesn't tell me why you think so. It is broadly plausible that Celts had some role but, as I said, this is not a mainstream interpretation of the facts.
You still find the vowel substitution in Celtic languages that have lasted until modern times.
You can do vowel and consonant substitution between almost any two Indo-European dialects and get the same effect, which is why we are able to determine the relationship between languages and can apply theories like Grimm's Law to language changes.
I am going to have to assume the "ium" part is a Greek or Latin suffix (after all, the Greeks got to tell the story).
It was likely something like "Wilios" in the pre-Homeric Greek. What you need to remember is that Indo-European languages have actually lost a lot of complexity over time and Hittite actually retained a lot of the phonetic features that linguists had long assumed should be there based on various sound transformations in surrounding parts of the word. That's one of the things that always surprised me about language evolution -- many languages seem to be getting simpler over time (e.g., English no longer has a dual case, nominative and accusative noun forms in most cases, etc.) which seem pretty counter-intuitive to me. Who invented all of the complexity in the first place and why?