I no longer use bead and cove. It is actually easier to bevel the strips. That is a topic that has been beat to death here. Nick and Rob have info on their sites and/or video about that technique.

If doing bead and cove, what I did in the past is to round one strip (where it was mitered) with a plane and use a round file to make the bead in the other. This is only for short miter joints. For your design I would cut the bead or cove off the strips facing the design and do the design in beveled strips instead of bead and cove.