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Eight words put D second and E third, and eight of them open with a vowel.
I opens three, A opens two, O opens two and E opens one. Between them that is the whole of the first box, so you are choosing among vowels rather than hunting for a consonant.
Both are common and both run IDEA before the final letter. Only the fifth box tells them apart, which makes them the sharpest trap here once four letters are confirmed.
ADEPT is the next most useful, followed by EDEMA and ODEON. IDENT, ODEUM and ADEEM are specialist and unlikely to be what a puzzle wants.
M and T each close two of the eight, and the rest take one apiece. With six letters appearing in the last box there is no ending worth betting on.
IDEAS is the more common word, so start there. If the last box comes back wrong, IDEAL is the obvious next move.
A small roofed theatre used in ancient Greece and Rome for music. ODEON is the same idea in a spelling most people have seen.
To revoke a gift left in a will, a term from law. Repeats are thin on the ground here, one out of eight, and ADEEM provides it with a double E.