I think you have the capacity, technical means and musicality to do a much better job then you did. For a moment I thought you might have been a little nervous and you turned to "automatic pilot", which is a good thing to have, believe me. But then I began to realize you hadn't really explored this sonata and delved into Mozart's dynamic indications and the reasons behind his choice of certain colors - subito forte, subito piano, pp to ff, etc. It sounded like a very superficial reading of this incredible sonata. I was so tempted to make a video and explain some of these things to you, but it would seem like I want to sit in cattedra and expound my theories.
The opening promised something good - the tempo was right, it flowed (I would play the first note as an acciaccatura, however) there was direction, etc. and then it just sort of slipped into a monotone and flat survey of the music. For example when the theme appears the second time, it has to be detached from that piano measure before. It's a reiteration of the theme and it has to sound like one. Not just a carbon copy. the second theme is piano and this gives you the opportunity to really project the direction of the running line: it goes up and down up and down. In the last five bars of the exposition (and again at the end of the sonata) where we have that nervous dotted rythm, play it first piano and then forte. Or something. And that tragic development where there are FF and PP,, I only heard a bland mf. To make it brief, I felt short-changed in the end. Like: That's all there is?!
The second movement opened up wonderfully. The right tempo (many play it way too slow) and very lyrical. BUT, that soon ended and you started playing around with the tempo and it began to sound a bit flippant. To me, all of the embellishments are melodic and need the appropriate singing tone and you took way too much liberty with the tempo. It just sounded to me like you hadn't really thought the whole thing out.
To me, the last movement was way too fast. It loses it's tragic nature at the speed you take it at. You take it almost in one. When it goes to c minor it says PP - at any rate, less then the opening bars. the forte that follows is SUBITO forte.
These are just a few observations to make you realize that there is much more behind this sonata then what you presented. And you definitely have the talent to play it. But my question is: re-listening to what you did, is this what you REALLY feel K. 310 has to say?