I've had both strains, but still, it is very hard to make sweeping, general statements about their attitudes. But, my experience matches pretty much what you're experiencing. The Reds can be tough as nails while the BSLs can be very laid back. This is too general, but.....
I'd shake things up. The trouble is that you don't likely have enough pens to pull off what I'd do. Still, you might extrapolate some ideas from what I suggest. Here it is. I'd divide the Red flock into two. Integrate the BSLs into half the Red flock. The sheer numbers of BSLs would cause them some security, perhaps. The Reds pecking order and flock size would be thrown into disarray. After a week, I'm guessing things would be ho hum. Then, I would put the flock all together. It would still be a sorting out process and sometimes, in my experience, the Reds as just plain mean.
Still, shaking up the dominant group allows the lower group a less powerful force to contend with.
