You're absolutely right, the possibilities in performance are always infinite, and researching into possibilities can go on for ever, for our entire lives! This is a wonderful thing, it means we should never be bored! My comments about the rhythm though are pretty general, and an attitude I have towards more or less any music I play: that they should be obviously identifiable, not contorted to the extent that they become something that they are not (like all the dotted rhythms in the 1st movement, as much expression as you add, they should never be confused with triplets, which is an easy mistake, and one you avoid to great effect!). However, while still maintaining their motivic identity, their function changes depending on what they are doing in the phrase, and it is always (I think) possible to make them work for you in order to achieve something that you want to express, rather than the other way around. My impression was that there are times when you sacrifice something that is in the music, that you even feel and would even naturally do, but that the sense of being "right" by the metronome diminished the space you allowed yourself to "play" with the rhythms. I'd draw more attention to, in addition to the obvious rhythmic motif (that holds together your rendition exceptionally well), also to the melodic importance of the semitone, which often I think can have more the character of a sigh. The sevenths/seconds, upon which the first movement is based, are the most expressive intervals after all. But to be honest, the places where I wanted more time most was when approaching big climaxes, where it seems to me you can prepare the listener by stretching the time a little. For me this doesn't erode the rhythmic integrity, but instead gives it more importance and functionality. The fact it's always the same rhythm means when it comes, it is always going to be recognized, and so the interest, for me at least, is in finding all the ways to vary it. The way you play does have that wonderfully impressive "machine-like" quality, as you mention, but I think without hardly any effort on your part, it could be much more expressive, and I'd guess still more engaging for the listener, to have a little more the impression that you are in control, in the driver's seat, and the music's saying what you want to say. From my point of view, even most macanical music can be better served as if it is the performer running the machine, and not the other way around, even if doing so shifts the listeners' attention from the technical and virtuosic aspects to more human elements.
You are 100% free to completely disagree, and in a piece like this, you are certainly not wrong to play it the way you do. But for the sake of another point of view, and possibly to illustrate better what I mean, I'm attaching a recording I made 5 years ago. The playing is not nearly as good as yours, the recording quality is horrible, and even the intentions I'm stressing in my comments here could be much better executed, but perhaps it's easier to follow at least what I mean with real sound as opposed to words. For some reason the 2nd and 3rd movements are on the same track. And the concert was on the unification day in Switzerland, and so at a certain point it becomes a contest between the fireworks and the piano... Something that strangely happened to me again this summer in Switzerland!
Anyway, like I say, I genuinely enjoyed your performance (more than mine for what it's worth), but as the discussion is for me an interesting one, I thought I'd post also my take, to see what you think.
ps - if you want to take a look at the Carter you can find it here: viewtopic.php?f=20&t=3671