We hear Coltrane going "outside the changes" in a fashion not at all untypical of his playing in this period. It is clear, however, that there is no merely mechanical superimposition of "Giant Steps" or "Countdown" harmonies, as is so often and so glibly asserted. Rather, what we hear in these two examples is a fluid and spontaneous chromatic prolongation of a particular governing harmony.
The term "prolongation" is borrowed from Schenkerian theory and is meant to suggest that the chromatic harmonies heard in these excerpts represent not simple substitutions but an elaboration of a single higher-order harmony that obtains over the course of four and five measures. To illustrate this I have verticalized Coltrane's melody, adjusted note register to idealize the voice-leading, and used Schenkerian symbols to highlight higher-level relationships. (In the graphs below, the bass voice is derived from the implied root movement of the melody. Accidentals apply only to the pitch immediately following.)
In Example A, the foreground cycle of chords (C-B-E7-A-C7) prolongs a C chord, the dominant to the tonic harmony of this blues in F. Prolongation of the dominant is appropriate since this phrase begins in the ninth measure of the form. The sense of orderly departure from and return to the governing harmony gives the phrase a kind of centripetal logic. Coltrane uses a chromatic upper-neighbor motion to prolong the conceptual top voice C while the harmony moves through the chromatic lower mediant, itself preceded by secondary dominants. The conceptual bass voice returns to C via the subdominant minor, creating a III-IV-V ascent that effectively prepares the subsequent arrival of the tonic.
The phrase illustrated in Example B begins in the eighth measure and prolongs an F-sharp seventh chord, which is the "tritone sub" of the dominant or the Phrygian II, spelled enharmonically.
In this phrase, Coltrane pivots from the F-sharp seventh to a local resolution on B, followed by an incomplete cycle of chords whose roots descend by major thirds (B-G-E-flat). The cycle is related to "Giant Steps," although in this case the major chords are not mediated by intervening dominant chords. Through this prolongation the upper voice C-sharp descends by step to B-flat/A-sharp. Here the F-sharp harmony returns and is additionally expanded, this time by a lower neighbor tone in the conceptual upper voice and a passing tone in the conceptual inner voice. The melodic tones of the last measure can be heard as 6-5-2-3 in F-sharp or as 4-3-7-1 in B-flat minor, the subdominant to the tonic F which returns at the top of the form in the following measure. The latter hearing suggests a particularly grave sort of plagal cadence, and the leading-tone transformation of F-sharp major to B-flat minor reflects the type of major-third relation that Coltrane explored to great effect in this period.
This rising third also inverts the falling third from earlier in the phrase. It is worth noting that in both examples, the goal chord reached before the return of the chord of the governing harmony is the chromatic lower mediant (A in Example A, where the prolonged harmony is C, and E-flat in the F-sharp prolongation of Example B.).
Also notable in Example B is the stepwise descending third motive, heard twice at the foreground level in the inner voice (F-sharp-E-D-sharp, then E-D-sharp-C-sharp) and once at the middleground level in the upper voice (C-sharp-B-A-sharp). The descending third motive is also suggested by the bass movement from F-sharp to E-flat on the middle ground level and more loosely (in augmentation) by the foreground cycle, B-G-E-flat.
In my view, these excerpts offer evidence of hierarchical structure in Coltrane's improvisations, inviting analyses that make use of Schenkerian concepts like prolongation.