sourdough with an unexpected result

I think a mature starter will make a difference, along with a long retard in the fridge. Some do the retard after, or as part of,  the bulk ferment and some recipes will have you retard after shaping. You can also cut the amount of starter used and ferment longer for more tang.

Sourdough doesn't have to be as strongly sour as S. F. sourdough.  My starter is years old, and my bread is still mildly sour -- I like it that way.  As Kingudaroad said there are things you can do after your starter matures.  Even now you can get more acid with retards.

Ford

I've been working for 6 months on getting my starter to a point it will make a "tangy" sourdough loaf. But, I kept having the problem of not enough sourness in my SD loaf. My starter would make a great yeast bread, but not a sourdough. There was much discussion on this subject in the forum and Debra Wink is very knowledgeable on this subject

I even started to add citric acid to my dough to develop a more sour taste.

With the help of this forum I believe I have now gotten my sourdough to that soured stage. My biggest problem was not allowing my starter to completely exhaust its food supply before I would feed it again. Basically, I had created a Baker's Yeast and not a Sourdough Starter. It never developed the acidity required for a Sourdough starter which should have an acidic pH of around 3.4 to 4.1. Any more acidity will kill the yeast. Less acidity make it more a baker's yeast.

Here's how I was able to change that and develop the acidity:

First, I started keepng my starter at 100% hydration, equal weight of flour to water. This is the daughter starter which I leave on the counter and use as my starter build. I keep the mother starter in the fridge and it's a stiff starter, around 50%. This is what I feed the daughter starter with once I use most of it for my dough build. I'll discuss the mother starter and it's maintenance later. I maintain about 300 grams of daughter starter. Once it has completely used up it's food, I remove 100 grams and discard it or use it to make pancakes, waffles, etc. Next, I feed it with 50 grams flour and 50 grams water. I would also add just a pinch of WG Rye, a couple drops of organic honey, and initially a few bits of Active Yeast, along with a few drops of either pineapple juice or vinegar just to help keep the bad bacteria at bay. Once you acidity level is where it should be, no PJ or ACV is necessary and remember PJ or ACV will kill yeast if you use to much. (NOTE: A few purist will say this is a disgrace, but this is how I developed my starter.)

My biggest problem was patience in the feeding cycle. You can read about the technical aspects of SD Starter elsewhere on TFL.

Anyway, after feeding, let the starter TOTALLY FINISH consuming it's food supply before feeding again or the wild yeast will not develop. There should be no yeast bubbles at all before feeding. It takes a few days, but eventually it will get there.

While 300 grams seems like a lot of starter, but a cup of starter is about 240 grams. And, with the starter on the counter it's not hard to get it boosted enough to add to your dough. That leaves a little to which I add my stiff mother starter, about 60 grams. This is 40 grams of flour to 20 grams of water. Add another 20 grams of water to make that 100% and then add 100 grams of flour and 100 grams water and let the process repeat itself.

Taste your starter. It should have just enough acidity to make you want to spit it out, similar to how you would react to a sip of apple cider vinegar.