Hide your Beethoven in the closet, or even better, replace that pre-Romantic deaf man with a truly Classical composer like Haydn, Kozeluch, Hoffmeister, Boccherini, Danzi, Paisiello, Pleyel, Myslivecek, Abel... And please, burn the damned cadenzas for K.466 as Hummel wrote way better ones and Beethoven's pitiful attempts ruin the otherwise perfect concerto. I don't know what exactly Ludwig did to Western music, but if I like the piece it means it's by pre-Beethovenian composer, with the only exceptions being Schumann's chamber music and Reger's organ works.
Mozart knew you have to keep the music clear. Double the voices if you need to impress, don't overfill the harmony. As someone wrote at the first page: Mozart's solutions are so natural you think they were completely obvious after you've heard them, but in fact you hadn't thought of them until they were played. This gives that heavenly 'ah, yes, this is exactly what was needed here' feeling of perfection. And that's not a matter of training as I felt that while listening to his first mass setting - he was still taking lessons from his father when he wrote it. It was a miraculous combination of genius, practise and musician-friendly environment.
Harmonic analysis of Mozart's pieces shows that they follow the rules of both functional and diatonic harmony and every chromatic twist is justified by a theoretical modulation (even if it lasts for a fraction of a bar). As that part of music theory wasn't known in the 18th century Mozart must have simply felt all of that - the conclusion is there was one more decisive factor: he must have had absolutely perfect ear, being capable of hearing all the interactions between the overtones.
Scientific analysis done by physicists shows that of all the major composers only Mozart and Chopin show such a consistency of overtone series distribution in their works, with Beethoven and Brahms being the most messy ones. So that's not really a matter of music theory, but rather of acoustics. Mozart felt what sounds good without knowing of the overtones' existence.