Hi anda,
On the matter of tempo, fear not, we all know and recognize that you played the Khachaturian Concerto, and played it very well too. The real issue is that artists have been debating Italian musical terminology since the time it first went into practice. I've always been guided by Josef Hofmann's advice: "Consult the state of your technique and your own feeling for what is musically right in deciding upon the speed of the piece." He also gives a caveat: "There is such a thing as 'artistic conscience'; consult it always before taking a liberty with the tempo."
The first movement is allegro ma non troppo e maestoso, or, of course, vivacious but not too much, and stately. The tempo marking per se and the qualifying mood have the potential of working at cross purposes.
The second is andante con anima or flowing easily with animation--so that seems a bit self-contradictory too. We generally think of andante as being a bit leisurely. Why did the composer not pick moderato or allegretto if it were also to be animated? These kriptic markings always cause pause for thought.
The allegro brillante in the final movement, lively and sparkling, is more straight forward, thankfully.
There are tempo changes within the movements which introduce more variables, of course.
But there is another dimension, where this is a concerto--the conductor. Some collaborative conductors will ask you what you want for a tempo. Others will take the attitude, "just follow me". As you know, these decisions depend on the seniority and stature of the piano soloist and the degree of the conductor's ego. Sometimes there can be negotiation and compromise, other times not. I don't know how that discussion went down before you first played at the rehearsal.
Another factor: I'm unsure as to which orchestra you played with and its degree of proficiency. At times it sounded thinner than, say, a robust 100 member ensemble. The conductor might have certainly taken the orchestra's proficiency into account too.
So, if those tempi sound right to you, and they are within or at least close to the general range of those you've encountered in recordings, then just enjoy your own recording! To me, the tempi sound fine. But, if you still have nagging doubts, try this: Get out the metronome and find the pace of your three movements and write them down; then do the same for the Kapell recording you like best, and compare the metronome readings. Try his out a bit at the piano. BUT, having satisfied your curiosity, do not necessarily be influenced by Kapell's choices! (Could he read Italian any better than you? Did he not also probably have some subjective notions concerning the tempi? One consideration though: Kapell and Kachaturian lived in the same era, and could possibly have communicated, one cannot rule that out; however, should the composer be the final arbiter?) So I again refer back to Hofmann here, meaning that tempo section is not without the individual artist's own perspective.
If you get to play this concerto again elsewhere, some or all the factors could very well change. So all the tempi might change too! It's good that tempo is so uncomplicated.
Topic: Khachaturian Piano Concerto