That EE is a pullet. She has a female specific coloration. Why do you think she's a cockerel?
What I would do- cross your largest buff orpington (I'm assuming you want larger chickens, not smaller ones?) with your largest RIR, then cross the biggest and/or reddest RIR/BO roo with the largest, most red EE hen (what color eggs do you want? Blue or green, or something else?). You'd probably get chickens that are close to or are the size of the orpingtons, with a mostly red color scheme, since red seems to be a pretty dominant color. They would lay greens eggs, assuming the EE parent was a blue or green egg layer. Then, if you wanted to improve size, cross the EE/BO/RIR to either a BO or an RIR/BO. If the red color was fading, cross the offspring to the reddest RIR/BO, unless all of them are too light. Then, if you need to improve egg color, pick the crosses with the best egg color and cross them back to the original EE/BO/RIR that has the best egg color, and if none of them do, cross them to an EE.