Conditional replace accented characters with non-accented ones

I want to be able to correct a specific type of mistake in Greek (free) text. For any word that starts with an accented vowel or εύ, if there is anywhere in that word another instance of an accented vowel, then replace the first instance with the non-accented counterpart of that vowel. It should respect capitalization and replace with the capital counterpart in case it is capital.

(In the attached file, 3 sheets, 1 with vowel list, 2 with example replacements, 3 with free Greek text with words for correction).

For example

Find Replace
άγώνας αγώνας
άδελφός αδελφός
άερόστατο αερόστατο
άθέτησις αθέτησις
εύρέσεως ευρέσεως
εύρύτης ευρύτης
εύχέλαιο ευχέλαιο

Accented Non-Accented
ά α
έ ε
ή η
ΐ ι
ϊ ι
ί ι
ό ο
ύ υ
ΰ υ
ώ ω
εύ ευ