Hello Alanna, I tested your suggested method in my lab today. There were substantial variations in strength for each cup and even greater variations in the amount of brew in each cup. It's hard to equally divide at this stage.
The way I've always done it is to press it all into one cup. Then add some water so the cup is about 2/3 full, stir, and dispense equal amounts into the three serving cups. The added water makes it easier to share 3 equal servings. NASA scientist Craig McReight taught me that trick. Finally, top off all three cups with more water to achieve American coffee strength.