For what little it's worth, my daughter got fluent in Mandarin in college plus travel, and she got back to me quickly when I emailed her today. The suggestion she gave was that it might be close to the short I in "chimney". Between that and your suggestion, I can kind of hear what I think I've overheard in conversation, a vowel sound that is kind of incomplete to an English speaker's ears and tough to replicate with any similar word. The rendering as "Chih" might actually be as good a guide as there is. Certainly my "Chee" would sound crude and uneducated to him. It seems there is general agreement on the second half of his name as "Way". But I had a colleague some time ago whose name was simply Wei, and he assured me you could pronounce it wrongly and have it mean something else three different ways simply by rising or descending tone, and I believe him.