Grilling is one of my favorite ways to do pizza - always makes a crispy crust, but as you discovered, it is best to monitor the heat carefully when you first use a cooker. We use a regular gasser at home, and Big Green mini egg when on the road. Either one produces great pizza.
One technique we use is to slap the dough onto the grill, then paint the exposed side with olive oil and then sprinkle with coarse sea salt. Once the crust firms, we flip it and then immediately load the toppings and cover. When you take a bite, you immediately taste the salted crust, which is especially good if you use smoked salt.
Your pie looks really tasty
