Isn't it great that there are so many possibilities in the baking world now! Four inch deep pans are wonderful when you make the right adjustments. You can't treat them like two inch or three inch pans.
The rule to follow on a four inch pan is to "bake low and slow". I would turn your oven down to 300F.
And with those pans being so small in diameter, I wouldn't use a heating core. Instead use 2-3 flower nails. They will still act as heat conductors, but not leave a huge hole in such small cakes.
Because there are so many factors regarding bake time (oven type, recipe, altitude, etc), you need to keep an eye on your first cakes and and check for doneness throughout the baking cycle and documenting for future use in your oven.
I'm sure you will love the benefits of baking in a four inch pan. You won't have to bake multiple layers. You will have fantastic height on your tiers, and they are a time saver.