I think it's a shame that I can only find one Sonata recording by Alfred Cortot. They say that he was considered a Beethoven expert early in his career. His playing (and masterclasses, for that matter) of the Op. 109 sonata is a spiritual experience.
I could be wrong, but isn't Beethoven remembered as a piano-crushing performer? Of course, much of his piano music is so intimate and introspective, especially near the end of his life, that it would require a much more reserved and meek approach to the instrument. In fact, if I remember right, Beethoven is responsible for much of the improvements made on the piano - such as greater dynamic contrasts and sturdiness. Weren't there even times where he would massacre the piano on-stage because of his musical fury?
If this is true, I would think that a performer such as Sviatoslav Richter would be more inclined to a Beethovenian temperament than even a pianist as respected as Claudio Arrau. With Beethoven, I feel that it is just as important to be knowledgeable about the historical context of performance as it is to have deep feelings about the music being performed. There is no question that Daniel Barenboim, Wilhelm Kempff, and Claudio Arrau have deep feelings about the Beethoven sonatas; but I feel that at their core they have restrained their musical demon to the power of their intellect. Richter, on the other hand, often lets the music carry him away to uncharted territories. THIS, I feel, is the true spirit of Beethoven.
Besides all this, however, my vote goes to Artur Schnabel. I am quite surprised that I haven't seen him mentioned much on this thread! Wasn't he a descendant of Beethoven? Not only do I feel that he captures a pure spirit of Beethoven, I also sense that his performances are as historically profound and accurate as is necessary. His tempi are usually very even and pronounced while also being alive. His phrasing is gorgeous and romantic. His rubato (an element which is only most understood by a true artist - Alfred Cortot and Vladimir Horowitz come to mind) is thoughtful and beautiful. Like I said before, I wish that Cortot had more popularized Beethoven recordings; but for now, my vote goes to Schnabel.
BONUS: I feel that Glenn Gould's Beethoven is inspired. Rough around the edges, spiritual, adventurous, and intellectually stimulating. His playing of the third movement of the Moonlight Sonata is, I feel, the best version out there.