Another thing you can do is separate the cod and abdomen plate and trim about an inch off the top of the cod and then reattach it to the abdomen. That would raise the cod piece up higher and not push the abdomen part higher under your chest plate. The belt will cover the seam and still mantain the proper shape of the codpiece.
What is it about having a codpiece discussion with a girl that just seems wierd.
EDIT** After rewatching that video, dont do what I just mentioned, I dont think that would look right, prolly best to trim and sand or pad the offending areas.