Oh yeah... very laid back and cool. I love this style. Have you now achieved your ambition? Does this meet the Viscount's conditions for an old style jazz standard? It certainly ticks the boxes for me. Although I do wonder if anyone actually wrote jazz standards intentionally (back in the day) - didn't they get stolen from shows and films and given a cool (or hot treatment) from many artists and over many years and many versions eventually become accepted as jazz standards?
I understand why you'd like to try this with a female lead. I think jazz is one area where female singers often sit better. Don't know why that is - and it's probably just a personal thing because I love Billie Holiday and Claire Martin and Julie London and Ella Fitzgerald and Helen Merrill and Madeleine Peyroux many more so much, and on the male front, there's Frank Sinatra (At The Sands is just great!) and more recently Steve Tyrell... Once you slip over the line into blues (and for me, most other genres) the situation reverses, but for songs like this, yes give me a girl!
That said, you do a fine job and I'm impressed and jealous of the vocal here.
The other thing about this type of song and arrangement is the expectations are really high. Even the most laid back of professional jazz songs are wonderfully arranged and the playing is always out of this world. I love the opening chords and the way this starts, but later when the horn section comes in it felt a little too simple and non-jazzy. I was also longing for a top class piano or muted trumpet solo. Now, none of this detracts from a fine song - I just think with a full on jazz arrangement and some slow burning solos (or fills), and with a girl singing you might find that, yes, you have achieved that ambition, because the song is there - the melody, and the words, and the subject matter, and the feel, and the changes. Yep, all there and very enjoyable.
My only other thoughts, and they're terribly minor, is firstly the use of the word rooster. That conjures up to me a rural blues scene, some old share-croppers on the porch and a rooster crowing. This (to me) is a big city, smooth, and sophisticated song. Folks deep within the city are more likely to be woken by... I don't know. But probably not a rooster. Secondly, the opening line suggests that the narrator is there at 5:00 but the girl he's singing to isn't - so she must still be in bed and has no interest in being up at that ungodly hour (I don't blame her), but the chorus is suggesting he's given her that option (you take the morning and the rooster) but the fact that she's not there at 5:00 suggest she has no interest in this. I'm not sure I'm making much sense - I just feel that there's something amiss with the logic somewhere.
But overall great. I love this style and would love to hear it with a female singer and some Miles Davis style muted trumpet!