Charming performances, Monica. I didn't listen to the first take, but the tempo seemed fine to me here. Tempo can lie in the shadow of a musically convincing performance. In other words, it won't break your performance if you have something special to say. If that's how you hear AND sing it, then that's how a piece should go.
I had a dentist that worked for me and she secretly learned "The Man I Love" when her husband wasn't home. She learned the piece just in time to perform it as a surprise birthday gift for him...
If you were accompanying a singer, the original Gershwin version would be more appropriate. I am not opposed to transcriptions as long as it adds to the character of the music, and not create a distraction. I remember mentioning my partiality to Wild's transcriptions in another thread. I feel that they are more colorful from a pianistic point of view. His Etudes convincingly inject life without sounding like a pyrotechnical display. In the suite, I also like "Fascinating Rhythm." It's a good extension of the Preludes. Hey, you've already recorded the Preludes, so I think you underestimate your abilities to learn the Wild transcription Etudes. BTW, I liked your arrangement of "They Can't Take..." It was seamless and smooth. You should do more arranging?!
In any arrangement, these songs will always be a part of the American musical culture whether it's in movies or musical circles. Your performance was evocative and the music was conveyed with deep feeling.