I agree with Akhenaten (EIE), although the typing is based more on a persona rather than any strong reason.
I think EIE for Homer, although that is also based on archetypal kind of reasoning. Typing him through his verse is of course highly speculative. (The same is true of Hammurabi).
Socrates (at least as portrayed as others) seems like he could only have been a SLI or an ILI, but if I was to type him, I would type him almost as though he was a fictional character, because we don't really have any direct and/or impartial sources about him.
I think I mentioned before that I thought Aristotle might be
-leading, but perhaps
-leading may fit someone who attempted an encyclopedic understanding of nature better. (I notice that at WSS, Pliny the Elder was recently typed LSE).
I'm wary of typing Xerxes as EIE, if he is only known through Greek sources, because there is a danger of him being described with characterizations from how Persians were perceived in general.
For some reason, I think Pericles has been typed ILE before, and Aristophanes EII: I don't have any strong thoughts on their type, although Aristophanes particularly has a rather discernible personality evident in his plays.
Alexander seems like he could only have been
-leading, out of all the people in history, so I can accept SLE.
Archimedes may have been typed ILE before, although this may also have been due to archetype\stereotype reasons.
Epicurus being
-leading seems fairly straightforward.
I'm not convinced that Spartacus could be satisfactorily typed.
I consider Cicero to have been EIE, his role in life seems emblematic of that type, although no doubt an ILE could feel at home in such a role also.
Caesar for SEE seems unproblematic.
I'm not convinced that Cleopatra can be typed one way or another with any level of confidence: I don't have any thoughts on her type.
Most of the individuals you've typed I've not thought about myself, nevermind attempted to type, so I consider your typings especially commendable. I am intending to read many dozens of biographies soon, although mostly not for people so far back, as generally only the very well-known individuals like Caesar get covered. I read a biography on Hatshepsut recently, and was not able to get a strong impression about her type, other than she was a woman who excelled in being noteworthy, in Egyptian fashion.