> My impression is that when you hear something aloud it's nearly always different to some degree from what you imagined in your head
For me and probably you, sure. For Beethoven, I seriously doubt they differed much at all.
The piano sonatas are ridiculously challenging and I'm more than willing to go along with you, but we could be wrong. I like your analysis and never thought about it that way. In general though as a (below-average) composer yes, I'm very certain about hearing things in your head. If I can do it he could do it with infinitely greater depth and efficiency.
About that particular piece, there's also the remote possibility of an editing or transcription disaster. He was not exactly thrilled with his publishers. More likely the former but I think you're right, the intent was probably there in his head.
No doubt they, like Beethoven, would be much more able to compose some if not all in their heads than i would be, but it doesn't mean they don't still find useful, at least sometimes, basic stuff that amateur composers do.
When I imagine music in my mind, the sonic qualities all seem the same as what I heard or hear, though sometimes I’ll mentally edit the arrangement intentionally or unintentionally.
I’ve also noticed that when I use my voice to sing melodies for compositional purposes, imagining the melody and singing are basically the same thing or have the same end result. On the other hand, using synthesizers and messing with patches usually leads to things I wouldn’t have always imagined in my head.
I’ve never asked anyone about any of this before, so I never realized others might not experience the same things. Sometimes I wish I could switch subjective experience for a day with another person to get real perspective.
I studied music theory and composition in college, so at one time I was at least somewhat practiced in reading and writing scores. My impression is that when you hear something aloud it's nearly always different to some degree from what you imagined in your head — and I don't think even someone like Beethoven escaped this entirely. I feel confident that he would have made minor adjustments to many of the late works he was never able to hear — he was known as a "reviser" in his working methods anyway.
My best evidence for this is the weird harmonic rhythm of the second movement of Sonata #32. ("Harmonic rhythm" is a technical term having to do with where we perceive a move from chord to chord.) The harmonies change at odd points. I don't believe that the effect was entirely deliberate — I think he meant for the harmonic rhythm to be straightforward and merely to anticipate with some melodic gestures. He was probably experimenting, but when you do something unusual, that's when feedback is even more important.
When I read that sonata, though, the harmonic rhythm I hear in my head doesn't seem off. The barlines provide a downbeat, and the apparent harmonies from the melodic gestures don't override it.