Cooking shakshuka without burning the tomatoes
I have a few suggestions: 


Use room temperature eggs so they cook faster. Egg white cooks at 150&deg;F (65&deg;C), room temperature is usually about 70&deg;F and refrigerator temp 45&deg;F. That difference is close to 50% more cooking time
Add a bit of water. Maybe your mix is too thick, if there isn't enough water in the mix it's more likely to burn, this dish depends on having enough moisture
Make your dents deep, get the egg as close to the pan as you can. Also, make the dents big enough that your eggs spread about a bit, more surface area means the egg cooks faster
Use smaller eggs so they cook faster
Keep the heat up more. I know it sounds counter-intuitive but if your pan is too cool you will lose a lot of heat at the top due to evaporation, the top will be cool but the bottom hot. Try a medium heat, but pay attention to 2.
You could cover the pan, I don't like this because you want the dish to lose moisture, but you could try it. If your canned tomatoes are very thick you may actually have too little water, so you could try keeping the heat low and covering it
Bake it instead once you put the eggs on, this will give an even heat on the top. It's not a traditional way to make it but if if you are results driven it may work for you