a little side note here, was this before or after the missions were changed to have same reward depending on commander level?
if it was after, then no, more power should technically not help or hinder it, because the reward (and thus the difficulty, or at least it better
) will be the same.
either way, ya, you will more then likely do better once you change all your weights to 8 or so, and transfer all that weight into the powercore, then use the extra power to further enhance your ship's systems.