Alkan's the man, 'nuff said.
Nice to see someone playing Alkan, and overall I think you do a pretty good job. I like your use of rubato; it generally serves to make musical points rather than being distorting, which would be the danger with bigger Lisztian rubato.
The one suggestion I'd make is an interpretative one, and as interpretation is inherently subjective, you're quite welcome to disagree with me. It's a general point applying to much of the piece, so I'll just use the first bar to illustrate it. I don't think it's "doux" or "chantant" enough. I know what I mean, don't know if I'm being terribly clear! Basically I think more of a foreground/background distinction within the individual bars would help putting it across musically.
If I was playing it, I would envisage the first bar as dotted minim B, quaver C, quaver D. With the tremolandi, I would play the melody note louder than the non-melody notes, and with the tremolandi pertaining to the longer notes, I would view at as the initial iteration of the melodic note in the tremolando should be louder than those which follow (which serve in my view as a kind of boost to the sonority.)
Edit which might clarify my idea: I've always felt that the first section is proto-impressionistic, and thus the tremolandi should shimmer.
You do know that Alkan was of some inspiration to both Ravel and Debussy? Debussy studied Alkan's Esquisses Op. 63 (and maybe other pieces) while he was in conservatory, and it can be reasonably be inferred that selections from it like "Les Soupirs" and other specific programatic pieces Alkan composed such as "Le Vent," "Super Flumina Babylonis," "La chanson de la folle au bord de la mer" or even "Le Chemin de Fer" played an impact on Debussy's composing to sound like nature and other specific moods.Ravel was an advocate of basically all previous French composers, and although I cannot cite the exact the exact source, concert pianist and Alkan authority Jack Gibbons said that Ravel had some scores of Alkan's music. The famous B flat tolling sound in Ravel's "Le Gibet" from "Gaspard de la Nuit" is also found in Alkan's "Morte" from "Three Character Pieces in the Pathetique Genre" Op. 15 composed many years earlier.