Mike I know exactly what you're talking about and it's one of the foremost reasons I was interested in your approach. I too try to strictly compose on paper as much as possible and stay away from both piano and computer other than to correct/check myself or on really difficult passages.
And on paper I feel, like you said, better able to visualize my music by using more areas of the brain for example as you said kicking in some sort of higher 'art' frequency and allowing that to help. What I mean by that is, sometimes on paper I don't simply get inspired just by the aural/sonic manifestations in my mind or inner ear, but by actual visual stimuli or mental/visual projections of how certain things "should look" on the score. And similarly alot of times on paper I do things you can't do in a notation software...for example many times you will get a fleeting idea that is so great that you can't hesitate even for a second to lose it because none of us have perfect control over our inner ear and so sometimes the grandest little flights of fancy and imagination can disappear within seconds and as such as I'm hurriedly rushing to notate it on paper I will often make otherwise inexplicable markings. As an example let's say I'm notating a melody in the violins and I want a certain accompaniment by the cellos that's very fast moving and sweeping, at the moment I don't want to focus on the 'craft' and mechanical harmonic/contrapuntal devices because as soon as I do I might lose that inspiration I just had for the original melody which I'm still writing as fast as I can before it disappears, so instead of turning that inspiration-channel off and focusing on writing the mechanical harmonic runs in the cellos, I might visualize the "MOTION" of the cello run as I can vaguely/distantly hear it in my mind so I will notate a vast sweeping line falling from the top of the staff then bending and arcing back upwards...then later as I'm done notating the melody I will return to that and actually mechanically place all the proper note lengths and accidentals and all that on this artistic sweeping 'line' that I just drew.
Also, many of the 'exercises' you mentioned in the star trek thread I myself have done though apparently not as regularly as you, but I try as often as I can to do all of the things you mentioned, well at least I used to more than I do now. But I used to listen to pieces and notate them as well, not exactly 'random' pieces, in my case it was pieces that were difficult for me to hear what the orchestration or harmony was so I would set myself up a challenge of trying to notate them just by litsening several times and then compare (well I wouldn't notate the entire piece or movement, usually just the first minute or two).
I also do speed exercises with my minor projects, for example if I'm working on something for someone, even if it has no deadline or a very loose deadline that's far away I will try to play a game with myself and pretend that the deadline is looming and give myself a certain amount of time to finish it. But by far my most important and regular (on a daily level) exercise is constantly listening to new music ACTIVELY, and what I mean by that is I never just listen to music for the sake of it, almost ALWAYS I am ACTIVELY attempting to decipher every single harmonic progression and orchestration that I'm hearing, and if I am stumped as is often the case then I will make an effort to locate the score and figure out how the certain effect was done that I couldn't figure out from listening. I too in a sense do this out of a slight fear of losing my hearing because it was only through his incredible skill of relative pitch and musical craft/technique that people like Beethoven or Smetana were able to continue creating masterpieces even after their hearing was lost because obviously after a certain point, your actual hearing becomes less important. I can write pretty decent pieces of work now strictly on paper without ever having to tap a single note on a keyboard or play into a computer because I know decent theory and can see and 'hear' each effect of every progression or note in my mind as it relates to the other notes and harmonies on the paper. This is sadly a skill that's dying fast and most modern hollywood composers like Hans Zimmer would not be able to even recreate Twinkle Twinkle Little Star on paper without the aid of a computer because their background is not of music composition but of pop and rock music and they don't have that extensive theory and ear training, they rely more on 'plonking away at the computer/keyboard' as Zimmer once said himself.
That's why I wouldn't be surprised if a large number of major hollywood composers are nothing more than really clever melody writers and rely more on orchestrators who would be more like you, guys that can compose their asses off in technical terms.
Oh and if it's any consolation, your method of composing preserves your hearing for far longer than the computer composers who are sitting all day long with headphones blasting their attempts into their ear drums. Similarly I'll spend half the time on paper in quiet solitude and am mostly on the computer only in the inputting/mixing stage.
It's amazing to think how incredible an inner ear and theory knowledge the masters of yore had. There are masterpieces like Bach's b minor mass for example that he literally never heard performed in his lifetime and yet it is perfect, that means he wrote all that wondrous counterpoint for so many voices without ever having the aid of a real orchestra or a computer program, it was done all through technique and the inner ear/relative pitch/solfege. Same goes for many works of Mozart, Schubert, and everyone else in between. Now that is a skill I envy.