I get the feeling of it not ever being quite there, so that's why I asked if you're happy with the way it's turning out. Your Pepsi challenge sounds like fun!
Cold ferment with 20% sourdough levain is a somewhat non-standard way to make pizza dough and I believe it's not very popular because sourdough fermentation doesn't thrive in a very cold environment. Even commercial yeast has trouble if the temperature of your fridge runs really low like mine which tends to drop to 32F suddenly (Thanks SubZero!). On the other hand, I have done many hybrid doughs with 10-15% sourdough and anywhere from a pinch to 1/4 tsp of instant yeast in the fridge, and didn't have any problems for 72 hours fermentation with Caputo Pizzeria. The longer you go, the more the gluten breaks down and the dough becomes wetter, more liquidy and harder to stretch evenly, so you can just go by feel here and try to find the sweet spot for your conditions. Personally, I think you'd be happier with either room temp/wine fridge sourdough only, or switch to a hybrid method if you're going to use the fridge and go past 48 hours.
If you use 20% sourdough, you're pretty much using a formula similar to Tartine bread - and that's fermented about 8 hours at room temp with amazing flavor. There's really no need for a 48-72 hour ferment with a 20% sourdough IMHO. But that said, if you want to stick to your current workflow, you can try Caputo Chef's flour, if that's an option for you. It's 13%+ protein and designed for longer fermentations so it should hold up better.