How do you know "Eli Eli" is not Aramaic? The fact those words exist in Hebrew doesn't mean they don't exist in Aramaic.

So I'm sure you may already know this, but the -i at the end of "Eli" is the first-person suffix, "my." (-i is a first-person suffix in both Hebrew and Aramaic.)

One (erroneous) reason that's been offered for why Eli in particular "isn't Aramaic" is that the shortened form of the word "God/god" in Hebrew is simply the two-consonantal אֵל (el) -- which the first part of Matthew's Eli matches perfectly -- while the etymological cognate of this word in Aramaic actually wasn't double-consonantal at all, but instead was the tri-consonantal אֱלָהּ, elah; and so "Eli" with nothing in between El and i couldn't represent the Aramaic spelling/pronunciation.

But while it's true that the tri-consonantal form of the word was the main one used in Aramaic, we actually do find bi-consonantal el used in Aramaic texts (e.g. in amulets and in magical papyri). Also, importantly, the best manuscripts of the Aramaic targum on Psalm 22 itself actually uses eli, just like Matthew does.

Funny enough, further complicating things here is in trying to explain the -o- in Mark's elo, in many ways this is actually closest to an alternate Hebrew form (אֱלוֹהַּ, eloah) of the Israelite God's name; probably a shortened form of the familiar longer form elohim. (To be sure, though, funny things can happen in the transliteration of vowel sounds. One thinks of the difference in spelling between the name that appears in Mark as Βοανεργές, Boanerges, vs. the likely original Hebrew/Aramaic of this; though there's also the idea that this spelling in Mark isn't just unusual transliteration of the Semitic original, but actually is a conscious assimilation to a Greek word.)

That being said, as for the Palm 22 quotation, it's still likely that Mark's is the earlier and original spelling, altered by Matthew.