Breeding Phoenix

As most people who are familiar with the Phoenix know, they're not the best layers and breeding them is more than difficult. That's what I need a bit of help on, I want the stronger birds the ones that are very healthy, I have an incubator and a brooder and my eggs are incubating. But if I want the best birds, what do I do? Phoenix aren't easy to breed and when you get chicks you have to be careful but what imperfections so I look for?

Inbreeding, what do I do there? How do I inbreed? For how long can I inbreed? One or two generations? I'm trying to get my hands on another golden Phoenix but as they're such a rare breed, finding one can be difficult. My cockeral is having good fertility and that's no problem but I only have one Phoenix hen, do I need more hens?

Thanks and I hope you can help,
William