If I put a lump of cat poop in a barrel, I can add more water, but there will still be cat poop in the barrel. So a purist will never be satisfied, and you can't officially call the offspring a breed, but at 7/8 they will be purer than most birds that pass for pure in the US.
If you take that pullet, and breed her to the RIR, and then keep a pullet to breed back to him, and then repeat as long as your pure RIR is alive, you can get pretty darn close. In fact, with careful selection for the traits you want, you might get something far better than a pure RIR. You could take the RIR back to it's former glory, when it had fresh Malay genetics, and it was still riding the hybrid vigor wave that entrenched the lore surrounding the breed. Malay is only an Asil misnamed by Europeans.
The RIR is a relatively new composite breed, but it has been bred out of the hybrid vigor stage. So you could be recreating, or rejuvenating the breed. You could call them improved RIR. But the purists, who think their RIR are untainted by hatchery birds with leghorn influence, would never be happy.
Do it. You could breed birds from the first cross together and do quite well. The ones that don't go broody will lay pretty good, the ones that do will raise replacements. I did a similar thing with Leghorn and American Game. Eventually you will have to add more game to retain the reliable brooding and effective free ranging features, as well as health, longevity and to get males that don't go nuts and try to attack their keeper.