| mark,
I would honestly recommend not playing the tune... as dumb of me to say as that might seem, that's just the way I feel about it.
As far as furthering your harmonic knowledge and melodic improvising ability over difficult changes such as giant steps.... I would recommend almost exactly the same process as I would for autumn leaves. You have to be in control of your instrument to the extent that you're able to play 1-3-5-7 (chord tones) on every chord in the sequence, be able to do that in all inversions, and be able to do it at all tempos that fall into your technical ability. This is just a very basic way into any tune where changes are moving. I would then make up scalistic exercises and triadic ideas based upon the changes just to have them in your muscle memory so that any sound you want at any given time is available to you to express your musical thought. I would be in control of the melody, be able to voice chords throughout the song, and be able to walk bass lines (no matter what instrument you play) throughout the changes for several minutes without repeating yourself.
I would then transcribe as many solos as possible of other people playing this song. Start with Coltrane's version as a basis. But kenny garrett, pat metheny, Freddie Hubbard, Michael Brecker, Brad Mehldau..... would alll be good places to draw vocabulary from.
It really isn't about the song, it's about how you can express your musical ideas no matter what the situation. You want to sound like you no matter what song you're playing. So Giant Steps may well be an important piece of jazz history, one which I highly recommend checking out without a doubt, but I would definitely put more time into working on your own sound, vocabulary and concept more than anyone else's.
Easy,
Janek | 
