How cooking temperature and oven set up can help prevent cakes from becoming too brown or burnt on top?
You said that you're using deep pans to get the right shape for decorating. If you're using something deeper than the recipe calls for, you should expect to have trouble. It will take longer to bake through, while the top and bottom overcook, and if you've gone too far, the structure may not hold up as well during baking. You can probably get away with something 25-50% taller than the recipe is meant for, baking longer at a lower temperature, but in general, you should really try to use the correct size pan, and make multiple layers if you want something taller.

Wrong sized pans aside, reducing the temperature is definitely the best first thing to try. In pretty much all types of cooking, burning some parts before cooking others is a sign of too much heat. You should also check the temperature of your oven. Ovens thermostats can easily be significantly off. If you're having this problem with multiple recipes, it's plausible that yours is too hot. Depending on the source of your recipe, it's also possible that whoever wrote it was compensating for a too-cold oven.

Also, make sure that the cake is centered in the oven. The top of the oven is hotter, and too high a rack can definitely cause overbrowning on the top. Of course, if you lower it too much, you may overcook the bottom.

Shielding the top with foil is also very effective. If it's just that this is a particularly sensitive cake, I'd definitely try loosely covering with foil. Protecting the pie crusts is such a common version of this that you can buy pie shields, rings of metal to cover just the outside edge.

I wouldn't try to turn your oven into a steam oven for this; steaming will affect the texture of the surface of the cake.