One thing that saved some time was using pre-grated carrots. They cost more but well worth the extra expense.
Lining the cake pans with wax paper was another time saver.....
After the cakes came out of the oven, a buttermilk glaze had to be drizzled over them. I messed up on my timing and did not get the glaze completed in enough time to get it on the cakes while they were hot out of the oven. I need to invest in a real double boiler and not having to rely on my makeshift one I use with two sauce pans stacked on top of each other.
Using the wax paper was great because I could lift the cake layers right out of their pans and get them layered together. Cream cheese frosting went between each layer.