Moo, singing tone is a myth. The only variables when playing a single note is volume and duration. So as pianists, we have to create the illusion of singing tone.
When the phrase "singing tone" is applied to the piano, it doesn't mean one is expected to be able to hold a note continuously with the same volume like a singer could.
When you say your teacher told you "when the melody is soft I should avoid striking as it creates a loud and harsh sound", then I'm a bit flummoxed. When the melody is soft, you have to play softly by definition!
The teacher was explaining(although not too correctly IMO)how to play softly.
One other observation. Each melody note is pedaled, so why are you hanging onto it? By keep your fifth finger in place, you are subjecting the rest of the hand to unnecessary tension and twisting that makes control of the accompaniment harder.
If you watch Zimerman and I'm guessing Horowitz and most every other great pianist play this piece, you'll see they hold these notes with their fifth finger and with the pedal. I think your approach would probably work but almost every professional holds the melody note down.