Catnip, have you considered the rotational method. I think that is kinda of what your are explaining. It was recommended to my by a master breeder, Don Schrider; he managed the buckeye project run by ALBC. YOu have all the lines to make it work. 3-4 lines, move the male from F1 pen to the F2 pen, and this doesn't cross back to fathers.
You can find more by googling rotational breeding. Place the new hens in a pen ,and when the roosters grow up, have a look at them and evaluate which pen of hens would best benefit from those genes. THe goal is to not double up on weaknesses.
THanks for the heads upon your notation of F1 f2, that is usually used to refer to the generations.