This has kind of already been answered but I wanted some practice plotting vowels according to their first two formant frequencies, so here's an attempt to confirm the sort of mid-ness of え using data. Note that it's all a sort of generalization since vowels vary quite a bit even just accounting for the speaker's head-shape and whatnot.
First, getting data from Japanese speakers on the Japanese え
I will be taking 4 samples per sound per speaker because that seems like a reasonable amount of work to subject myself to. I'll be looking for samples which have a clear, long え vowel because they'll be easier to accurately find the vowels in.
List of Speakers:
StrawberryBrown (took 映画, 英語, 撮影, ええ)
sorechaude (took 英語, 遠征, 工芸, 中米)
chiharu (took 個性が豊かだ, 規定値, 優越性, 統計図)
poyotan (took 書影, CADデータ から2Dモデルを作成, 四カ年計画, 低刺激性)
skent (took 先制, 属性, 聖ヨハネ, 繁栄)
I analyzed each of them in PRAAT and the formant frequency data can be found here.
This chart shows how they all look in a vowel space. Ignore the numbers Excel puts on the axes. They're just the minimum values
I'm (as far as I can tell) using the same set up as this except in Excel which doesn't make quite as nice of a graph. (x axis 1300->150, y axis 2900->375, logarithmic scale)
I then initially decided to gather data on English words with e and English words with ɛ without realizing that the two symbols refer to the same phoneme in English. I got them both from searching Forvo for let, mess, neck, deck, pet, and tell.
Here are the two overlaid.
I did try in the end to find at least one example of an actual ɛ and used the Wikipedia recording to get this yellow dot above the Japanese data. (Ignore that one of the other dot types reverted colors please.) The ɛ is ostensibly supposed to be above the e and the e below the ɛ, so I'm not quite sure how to interpret this, but it probably seems at least that the Japanese え is separate from e and also from ɛ and maybe somewhere in-between
Edit: Actually the e that corresponds to ɛ is in fact supposed to be below the Japanese え, so this makes perfect sense. (Since they're actually all ɛ, probably) The "e" that would be probably above the Japanese え is the one in bait. I have no idea why there's such conflicting information on what's an e and what's a ɛ (are dialects quite that varied?) but I'm certainly not the person to sort it out. Questionable now is why the ɛ from Wikipedia is above the Japanese samples though