In my opinion, these don't feel right syntactically.
Aaron: First of all, I can't think of cases in which a yud is ignored completely during translation and not turned into a Y or a J, especially when it's from the element yah. Names that begin with this element also have a vowel sound right after it (
Yehonatan, Yehonadav, etc.) and don't jump right in with a glottal stop that would render the name unpronounceable. If you want to add these elements together you'd get something like Yaha'aron which is not what you're aiming for. Additionally, the meaning you're looking for has a perfectly good phrase already, in which the words are in the opposite order (aron adonai). So, all in all, this meaning and spelling for Aaron/Aharon is a really big stretch, and feels very wrong to me.
Elijah: I don't feel as though 'eli + yah would get an E sound at the beginning, that feels very odd grammatically. On the other hand,
Aliyah exists as a word and does not contain the yah element so I am not sure what it would turn into.
Elijah feels like a stretch to me.
Anyway, I'm sorry I'm not an expert on ancient Hebrew or linguistics so I can't give you any actual analysis (or anything much past a gut feeling). I hope this helps.