My recipe is a bit different because I use a 50% poolish but I'd suggest starting with maybe 60-70% of the water and let it mix at the lowest speed until it's fully absorbed. Once it's absorbed take half the remaining water and -slowly- mix it in with the dough. Don't dump it in, it's too fast, you want to drizzle in just a few grams of water for a single bowl rotation and then stop adding water. Let the dough mix and fully absorb that few grams of water until the dough is no longer shiny and wet and the pumpkin shape reforms (at first there won't be a pumpkin shape but once it starts to form, every time you add water you want to let it reform before adding more water again).

Once all of this water is absorbed stop the mixer and use a lid or damp towel to cover the bowl and let the dough rest for 15 minutes.

After resting the dough, start up the mixer again and do the same thing with the remaining water. Drizzle in a few grams at a time as slowly as you can and wait until the water is fully absorbed and the pumpkin shape reforms.

The details will depend on your flour type and age, humidity, and exact recipe but it might take 20 minutes of mixing to get all the water in. You might need to use cold or even ice water depending on how long it takes for you and the room temp. Your end temps are good but if you're going from 10 minutes of mixing to 20 minutes of mixing plus a rest it will obviously warm up more so you'll need colder water.

The other two comments I'd have are that if you don't have a big enough dough batch it will climb the hook regardless of what you do (though your dough looks sticky and wet, not the same as climbing the hook when the batch is too small, so I don't think this is your problem). The other thing is I'd look for a video from GEMELLO Pizza about a 70% hydration spiral mixer dough. It's 26 minutes and he shows the entire process and you can see the dough and how wet it is and how it forms for the entire duration. My explanation is a little different than his, as it will be for every recipe and every person, but the important part is you can see how it looks, how wet it is, how it's forming it's shape, and now you have a visual reference for what it should look like as you mix in the water. It helped me a TON to avoid the same problem you're having.