This is how I do it, others might do it differently, people's brains work in different ways, you have to find the way that works easiest for you.
I keep the running count seperate. As already pointed out, You only need the running count (in order to convert to true count) twice a round. Once, when you are about to bet, and then when you play your hand.
So I add up all the exposed cards (canceling out pairs, etc.) I then take this total and add it to the running count (the count I was left with at the end of the last round, or whatever) which I store seperately in my brain. This becomes my new running count total. If any more cards are exposed, I take the total of them, and add/subtract it to the seperately stored running count.
There is a certain pace that cards get exposed in, and you get used to when to sum exposed cards, and when to add that sum to your running count.
Be careful, when the dealer flips a blackjack! Then you are going to see all the cards at once, very quickly, while the dealer scoops them all up. Remember to moan real loud like a ploppie when this happens.