Avant-garde style, yet Greek vibe?

Helvetica Neue
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To me, that's two custom jobs, top one on Avant-Garde Gothic and bottom one on Helvetica Neue.

The top is 99% solved, I'd really like to have the capital A's bar on the bottom. Any fonts with that feature that's similar to Avant-Garde Gothic?

The bottom is spot on!

Sorry, don't know any Avant-Garde with such a treatment but that's actually not a problem as it's not difficult to reproduce: separate /R leg from counter, /E crossbar from vertical stem, remove /A crossbar and reuse it at the bottom.