A Dvorak variant for polytonic Greek:
'~ (, ). Ππ Ηη Φφ Γγ Χχ Ρρ Λλ ?/ += |\ Αα Οο Εε Υυ Ιι Δδ ἀἁ Ττ Νν Σσ _- :; Θθ Ωω Κκ Ξξ Ββ Μμ Ψψ Σς Ζζ
This is reasonably mnemonic for Dvorak users. It differs slightly from Beta code in order to keep all vowels on the left-hand side of the keyboard. Here, Yy=Ηη, Qq=Θθ, Jj=Ωω, Ww=Ψψ and Vv=Σς are somewhat arbitrary, and the mappings c=Χ and x=Ξ are swapped in Beta code.
This keyboard lacks the iota subscript, the grave accent, and the diaresis. The quotation-mark key is used for acute accents and circumflexes, and the "Hh" key is used for rough or smooth breathing.
This input method is relatively usable, but it could still use improvement if reimplemented with an X input method instead of an Xkb keyboard layout. H+vowel at the beginning of the word would indicate rough breathing, and the vowel alone would be used for unmarked breathing. Medial sigma would automatically change to final sigma when followed by a space or punctuation. Underscore+i could be used for subscript iota. Alternatives for some letters would be nice too; "th" for theta, "ps" for psi.
Another Dvorak-like Greek layout, but for modern Greek: https://unstable.nl/andreas/el_dv.html