Two things control the acidity of a starter. The first thing is the feeding frequency and amount. If you feed the starter, wait for it to double and then feed it again; you're are basically not allowing enough time for the acidity to build up. Also, the food-to-starter ratio affects acidity. The higher food:starter, the less acidity and vice versa. The second thing is the activation temperature, you will see in thefreshloaf.com that some users advocate the lower temperature for more acidity while others would advocate higher temperatures. I think it comes down to the starter type. For the Ischia I found that lower temperatures produce more acid flavor.
You have basically taken you starter from one extreme to the other. It was very acidic and when you built up the new one, you lost much of the acidity. With time, it will be acidic again. The next time you decide to decrease acidity, you probably want to save more than a cup. For your current starter, you can increase acidity by allowing it more time past the full activation point. If it doubles within 4 hours after feeding, allow it an extra hour.
Embarking acidity in the final product can be done in many ways If you see how sourdough bread is made. It's also relative to the starter itself. What struck me reading breadmaking material is that it's not common to make sour products with long room temp fermentation using a one-stage dough. I am really questioning the method that seems to be popular on this forum and I use myself. We make a one stage dough using fully active Italian starters as per Marco's recommendation while I remember one of his posts saying that pizza is not supposed to be sour because it's not bread. His method basically uses the Italian starters as yeast for leavening the dough.
If you notice sourdough bread recipe, you will see that after a starter is brought to full activation, the next step changes things. Some of this fully active starter is used to make a pre-ferment. The type of pre-ferment is what makes most of the final product's flavor and acidity. The pre-ferment is then incorporated into the final dough. The pre-ferment is basically your flavoring/acidity agent.
Here on this forum, we are basically using a small amount of a fully-active starter directly to make the final dough that we anticipate to be sour. Why do we use a dough making method that treats the starter as yeast and expect a sourdough product? Are we basically making one big pre-ferment and baking it? Are there any implications to this approach? advantages? I really don't know but it makes sense that we can get acidity if we go this direction. Like I said, inducing the acidity in the final product can be done in many ways. Which one is right is for you to decide but I still question why the popular method in the forum is not seen much in sourdough breadmaking recipes?
It is certainly something I will be investigating when I'm done with my current addiction to NY,18" long room temp fermented dough