Tempo for this movement is a complicated question. The current thinking is that Beethoven probably intended a faster tempo than is typically performed nowadays, and I believe one authority even suggested it should have an alla breve (cut time) feel to it. But I prefer to play it a hair slower than the Kempff performance you linked. What is correct? I am of the view that if it works musically, then it's not 'wrong', so if you think it sounds good at the Kempff tempo, I don't think you can be faulted for playing it like that, especially since you seem to desire to being out a lot of detail.
Unfortunately, I am also of the opinion that it is impossible to truly learn how to play the piano on a 61-note keyboard. It's not just about the number of notes, it's about the feel and infinite variation of the keys, which nothing but a real analog instrument can teach you. You remark on the sound of the Kempff performance, and learning how to control and balance the sound of the different keys and voices is a huge part of piano playing. When I have my students practice this piece, I usually ask them to try different balances: Melodic line slightly louder than the triplets, melodic line prominently louder than the triplets, left hand moderately balanced, left hand very quiet, etc. Controlling the balance of two voices in the same hand is NOT EASY, but is essential to learning the piano properly, which is why I always challenge my students to do it.
Please note that I'm NOT trying to discourage you from practicing of your keyboard! By all means, keep playing, just realize that there are some limitations. If I were limited like that, I'd probably concentrate on piano music originally written for harpsichord - Bach, Scarlatti, etc. - which more closely approximates the attack of an electronic keyboard. As far as the range limitation goes, I'd probably just fake the bottom pinky notes in the Moonlight, instead of playing one octave higher.
Hope that helps.