Greek pronunciation

I am happy to report that I don't remotely speak Greek, but I am developing an understanding of the accent and can read a menu comprehensibly.  That said, I confirmed with our wonderful receptionist at our current hotel that we are, in fact, pronouncing the girls names more or less correctly, with only minor modification of the vowel.

Metis seems to have a more open "e"
Mnemosyne would have more emphasis on an open "o" than an "ah".

But I did learn that "mnemosyne" is a ritual in remembrance of the dead conducted 40 days after the death.  So, while our the receptionist thought the name odd and perhaps a bit socially awkward, it is all the more appropriate as she is named in memory of Persephone.