It is an excellent idea. Hybrid vigor usually takes over with mixes.
Yes, never breed forward an animal with an obvious health flaw (unthrifty, cross beak, wry neck), but with mixes, there is less chance of having a recessive match up. You get that with a number of pure bred lines.
If you place your RIR rooster over those ISA hens, you essentially are furthering a Production Red line. Really good egg layers, not so good for meat. Should all be red colored, both genders.
If you place your BR rooster over your ISA hens, you again will get good egg layers, though not as likely as prolific as the RIR/ISA. They will be hardy birds that lay well. A bit better in body weight, but not a truly dual purpose bird for meat and eggs. With the rooster being barred, all chicks will be barred, single copy, both genders. (Breed those BR/ISA girls, first gen F1, back to the barred rooster and you will get double barred males, single barred females....breed those F1 BR/ISA barred females to the RIR, and you will create black sex links...boys single barred, females black with red leakage.)
It is an excellent project. I have had great success mixing pure breeds with commercial hybrids (ISA/Red Star/Red Sexlink/California Grey).
Just be sure to always use your healthiest, strongest, least problematic birds. I would settle in with that flock and those 2 roosters for a number of seasons and select for the best of the best to set you lines of fine, home brew egg layers.
Shout out to Tennessee...lovely country. My daughter and her husband are organic farmers in Tennessee. Love visiting my grandbaby there
LofMc