Don't be scared about those tins, they are easy to use. It is just that they are better to be used for the sort of recipe they are designed for. Try 'Googling' Traybake Recipes, you will see that there are many, many cakes to chose from. It is great for Brownies.
Same heat & just check it after the same amount of time. If, spread out, it would be the same depth as in the smaller tin then the cooking isn’t going to be different. Just check & put it back in for an extra 5 mins if it isn’t quite tight