I have no real experience with carrot cakes, but I ALWAYS line my pans (bottom and sides with parchment paper cut to fit. If the parchment on the sides is higher than the pan the cakes will tend to use that to"grow higher". Carrot cakes are heavy though so you might need more specific advice with those. Also when in doubt I bake at a lower temperature (170C) and then test in the center with a toothpick every 10 minutes starting at 40 minutes. A 6 inch cake will often need 50-60 minutes at that temperature. When done, if there is a dome in the center I gently press down with parchment paper while the cake is still hot. Magic … no more dome and very little if anything to be trimmed off at the top. As soon as the cake has cooled a bit but still quite warm, I depan, wrap in saran type wrap, aluminum foil and a nylon bag. Then I freeze it overnight when it is much easier to handle and can be sliced without falling apart. I’ve never used heating cores, but tend not to bake thick layers. I much prefer to take a full recipe of cake batter and to bake half each time. That way the cake can bake thru better and it also saves me the chore of splitting into layers. Maybe this last idea would be helpful for you. Best wishes :)
The Garden Baker