what about...
you wrote
"You are correct that with some positive true counts dealing another card is more likely to result in a fall in the true count than a rise. Note that such true counts are the more extreme ones. For example, consider a hi-lo true count of +20 with 1 deck remaining, and assume that this deck contains 30 big cards, 10 small cards, and 12 'mid-sized' cards. In this example, dealing the next card will cause the true count to increase 42.3% of the time (when either a small card or a mid-sized card is dealt) and cause it to fall 57.7% of the time. For more moderate true counts, say, +6, the true count will be more likely to rise with the dealing of one extra card. For example, if a deck contains 23 big cards, 17 small cards, and 12 mid-sized cards, then a rise in true count will occur 55.8% of the time and a fall the other 44.2% of the time. It's true that for any positive true count there is a higher probability of a big card being dealt than a small card, but dealing a mid-sized card causes a slight rise in true count."
However, what about this case:
playing in a DD game, using 1/2 deck resolution (or 1/4 if you choose but 1/2 makes it simpler for the moment). Take your TC of +20 scenario with 30 big cards, 10 small cards, the rest are 7/8/9.
Currently the TC = 20/(2/2) if we are doing our TC resolution to 1/2 deck accuracy. Or TC=20. Now we have 3 cases...
30/52 of the time a big card will come out, and the TC = 19/2*2. 12/52 of the time, a small card will come out and the TC = 21/2*2 = 21. The remaining 10/52 of the time, the TC doesn't change, _except_ at those step-function points where the denominator changes because removing one more card causes our half-decks remaining to drop by 1, making the TC jump.
So, the original question was "is the TC more likely to rise or fall if it is already positive?"
It sems that with the above, 30/52 of the time it drops, 10/52 of the time it rises, and 12/52 of the time it is unchanged. Except, as we cross a remaining-decks resolution boundary, it is likely to rise since the denominator falls.
Now we are left with this: 30/52 of the time it drops as a big card comes out. 10/52 of the time it rises as a small card comes out. And 2/52 of the time it rises as we cross the boundary to a smaller number of 1/2 decks remaining.
If all that makes sense, then it is more likely that a high TC will drop, than it is that a high TC will get higher, which was the original question. If we go to 1-card resolution on the remaining deck estimation, then it becomes a pure function of the ratio of big cards (which if they come out the TC drops) to the non-big cards (which if they come out the TC rises).
Does that seem reasonable???