John Coltrane Giant Steps Live - Where is it?

Yes, the chronology is noteworthy.  Ellington was a fount of musical knowledge, inspiration and sophistication - of which, both Davis and Coltrane were well aware.

(Although the broken English leaves something to be desired,) this excerpt from the musicweb site is informative:

"Composer: Duke Ellington (1956). Recording: 'Blue Rose', Rosemary Clooney and Duke Ellington and his Orchestra.

Harmonic topics:

'Blue Rose' is an easy introduction of the 'Coltrane changes' ('avant-la-lettre', 'Giant Steps' is composed in 1959). The medium slow tempo enhances the feeling of three equal key centres (F, Db and A major). The tonal connection though, is pretty strong because of the descending progression: each next key centre sounds like a bVI degree to the previous. From bar 13, an harmonic sequence starts from the subdominant key Bb, but stops at the first 'Giant Step' Gbmaj7. From there, Gbmaj7 becomes Gbm6 (IV MD) and moves in a plagal progression to Dbmaj. This key is also major third related with F major, the initial key centre of 'Blue Rose'.

In 'Giant Steps', the complete cycle of ascending major third related major key centres is presented in bar 9-16 of that particular tune. The idea of three equal key centres is in Giant Steps even more present because the ascending variant feels less 'natural' than the descending cycle (introduced in Blue Rose, a couple of years earlier by Duke Ellington).

The trumpet introduction with the parallel seventh chords (Gm7-Am7-Bbmaj7-Am7) seems to be the model of the later 'Milestones' (1958, Miles Davis): same chords and top note, even the rhythm is almost the same.