Just trying to determine if maybe his grip is off or if the bench isn't working certain muscle groups enough. For many people, the triceps would actually get pretty fatigued while the chest may not, especially with some arch.
The goal is to make progress on intensity day, so if your volume is a ball-buster, consider reducing it. I'll post the same article that was suggested to me. You'll definitely have a d'oh/duh moment when you read this
Understanding the Texas Method Intensity Day | Andy Baker
I was just curious as to why you'd want to add CGBP in a program which already stresses the triceps via bench and press. Both use the anterior delts and triceps, so if anything, I'd expect you to say you want to do wide(er)-grip bench to work the pecs more.
Looking at your program, you're trying to set PR's twice per week. Once in press and once on the bench and pretty serious volume for both. You don't give your body time to recover. Not to mention the squat/DL maxes. That's a lot of stress on your body. Hopefully you eat like a horse and get plenty of rest.
I'm not a programming guru, so I'll let someone smarter chime in and help you with your programming, but it just seems like a bit much to me.