Are you sure you only need to play one movement? Most schools I've looked at require the whole thing.
with your timeline, I suggest you go with a slower movement, generally the faster ones take a bit more time for the finger kinetics to gel...have a listen and read through the 2nd movement of the Mozart Sonata No 2 in F major the 3rd movement was suggested above, the slow one is so pretty and very effective when executed properly, really really lovely, pianist, Uchida.
I find the 2nd movements of sonatas harder to learn than the first movements or the third movements. It's a bit tiring to hear time after time that the 2nd movements are the easiest when really they are more like the hardest. Remember that music is not just notes and just playing the notes won't get you anywhere.
Ah I see where you are coming from, according to the timeline a second movement would be easier to get under the fingers. However I disagree that speed and accuracy usually take longer to get under your fingers than musical interpretation. Everyday in the practice room one can find something to refine about their interpretation no matter how long they've had the piece. It's a huge risk playing a piece like that - impressing the judges is based purely on interpretation and musicality and if one is lacking, then it most certainly will not impress the judges. It's sort of an all or nothing with that sort of piece. However, I do apologize for being antagonistic, it was a stressful day yesterday. You shouldn't accept half the blame, it was my fault for making assumptions. In the future I shall be politer.