It sounds like you have all the elements ready to make fantastic pizza. I agree with you that all the separate components are difficult to put together into a cohesive workflow. There are just a few things you need to know to get started.
1) You can make amazing pies with KABF, you just need to pay attention to the protein level (~12.7%), which is higher that most normal AP. That means you need to get the mix stage right so you are developing the gluten to it's best potential.
2) Your sourdough starter might do better working at room temps. Using a smaller percentage of the starter will allow you to keep the dough for extended periods of time, and then use the fridge to cool it down as needed towards the end of the ferment. This gets you that flexibility you are after in terms of bake time. I am assuming a room temp of around 70 degrees. If it is much higher, your ferment times may be shorter.
Here is a basic recipe for high heat cooking. You can adapt this in any way you want, as this is not the only way to do things:
KABF Flour 100%
Water 62% <-you can go higher if you want, and feel comfortable with high hydration doughs
Starter 10% for 18 hours, 5% for 24-26 hours at room temp
Use the site dough calculator to get your recipe size.
Put 90% of the water amount in a bowl. Dissolve the active starter in the water, and then add the flour. Mix with your hands until incorporated. Let sit (autolyse) for 20 minutes. Add the salt and the final 10% of water (sorry Calvel!). Squeeze it in until incorporated. Let sit 15 minutes. Grab a side of the dough, and pull it over onto itself. This is a stretch/fold. Rotate the bowl and do this 3-4 times. Let sit 15 more minutes and repeat. Repeat again as many times as needed, until the dough seems more smooth and elastic. Bulk ferment for half of the total time frame you are using (including the time stretching), and then ball the dough for the remainder of the ferment.
Do the same as above through adding salt and final water. Mix on the lowest speed for 3 minutes, and then on the second speed for 4 minutes. This is called an "improved" mix. But you should note what your dough is starting to look like during the second stage. You want it to just start to look smooth. If you go too far, it may over develop the dough. When fermenting at room temp, I like to let the yeast have a chance at some gluten development. Your mixer type will also have an effect on how fast the dough develops.
If at the end of your ferment you notice that things are starting to ferment too far, you can always park your dough in the fridge for 15 minutes to slow fermentation down. You can also put the dough in the fridge for the entire balled stage if you like, and watch it's development to see when it is ready.
You can cook this dough in the 700's with ease, just make sure the heat from above is enough to cook the top as fast as the bottom (to avoid your bottom burning). I would not go above 800 though, as the KABF is malted.
Have fun and let us know how it turns out.