There seems to be a disconnect between "improvise in most styles" and "harmony is grammatically correct." If your improvisations are stylistically good, are you aware of what you are playing in the sense of harmonic grammar? Can you imagine an improvisation idea, and then play it? That's audiation. You could try to audiate, then write the idea down first. Play it after to sort of "test" yourself. Or you could try a mix of improve that you then transcribe along with audiate (hear it in your head) then transcribe that. You could use one mode to correct/adjust the other. Improve at the keyboard would then become improve on paper.
Is there a method of learning how to hear chords in your head by reading a score that anyone is aware of?
I would say the reading method to do that is sight reading. But I think it would be better to describe it as "hearing chord changes" rather than "hear chords".
When sight reading you look for relative changes, and those relative changes should be read for both execution, basically fingering and position changes, and aural changes, how it will sound.
Think about this: if you didn't have an idea of how the music you sight read should sound, how would you know if you are playing it right? You have an instinctive sense of it sounding right, but you want to cultivate that into a deeper sense of understanding. For example, you're reading something and playing the tonic chord, a part of the music moves from the tone SOL
up a step to LA
, your harmony studies tell you it's moving to the subdominant, repeated sight reading and listening will eventually allow you to hear it in your head before you play it.
After you have done a lot of sight reading, when you write something on paper (in the style of whatever you've been sight reading), you should be able to know what it will sound like before playing it, what it sounds like as you write it.
You want three things to eventually become linked the eye for reading, the hand for executing, and the ear for hearing. Composing to paper directly, without actually performing, essentially becomes the reading part extended through a creative impulse. With enough training in the style of the writing, your trained hands and ears will have a good idea how the writing should be played and sound before actually playing the music.