There are a view things that I can think of, that influence the aroma of a sourdough baked good (and for sure some more):
1) The flour you use
2) The hydration
3) The amount of sourdough used
4) The temperature
5) The starter symbiosis
When you read this forum, pizza is often made with the direct method. Also called 0-step method. This means you don't build a levain (or "build it in 0 steps"
) and use the starter directly in a small amount in the final dough. Therefore you cannot change the hydration and the flour you use.
Rye would give more sour and aroma. Also a stiffer dough would last longer to ferment and be more tangy.
The amount of sourdough in the direct method also usually is too small to have an effect on the tanginess of the final product. With bread you can built a levain (sourdough) that has up to 33% of the final flour (for wheat, even more for rye) already in it as a preferment. This preferment can be overprooved and therefore have a lot of tangy taste and flavour that it adds to the final dough. As you will add a lot of flour to the final dough, the overproofing of the final dough won't matter for the final rise.
You can do this with pizza as well, but not the whole 33% as the gluten in the preferment will get weakened. Craigs wonderfull table also might be off.
The temperature is something you can adjust. In general: The warmer, the more active the microorgansims, until it gets too warm for them and they start to die. But: this is not linear and the increase of activity and metabolism is different for different mos. At 26°C the yeasts perform best compared to the others. Above that, more and more lactic acid is built (the fruity aroma) and below that, more and more acidic acid is built (tangy taste).
For bread baking some use a 3-step built of levain where at each step the levain is held at a different temperature and different hydration that all wanted aromas are there and the yeasts active. I use a 1-Step method with falling temperature form 30°C to sometimes 20°C sometimes 18°C. Again for directly built pizza this is difficult to time and I wouldn't do that.
But what you can do, is lower the temperature to maybe 18°C and prolongate the proof and then try if it is more a tu gusto.
The starter symbiosis:
You cannot switch out the microorganisms that are in the starter, of course.
But you can influence their balance with all the things from above. I for example mostly use a rye starter to inoculate the wheat sourdough for my pizza. It gives me the sensation of a fuller aroma.
In Italy, a 100%-starter is almost unknown. Usually they are at about 50%. This would make them more sour in theory, but they are refreshed with much more food (1:1:0.5 - starter:flour:water) and kept warmer before being fed again and then stored in the fridge. Also they are often kept under pressure like a sausage or under water.
In Italian language, but take a look at the pictures: http://blog.giallozafferano.it/fablesucre/lievito-madre/
It can happen, that the starter almost tastes sweet.