Unwanted eggs

[gmgallen]

I have two six-year-old cockatiels, one male (normal grey) and one female (lutino). I was under the impression they were both male until an egg appeared at the bottom of the cage. In my defense, Lutino cockatiels are tricky to sex. These eggs I am absolutely certain are not fertilized and never will be. The male cockatiel is absolutely infatuated with his reflection and all of his affection is directed towards his reflection. The female would like to mate, and is receptive, but is always ignored by the male. Anyway, this happened about 18 months ago in December while they were in their smaller, old cage. I let her lay a full clutch of eggs and then both birds and eggs were moved into a larger cage. After that, she took no interest in the eggs (likely from feeling too insecure in her new environment), so I threw them out.
Now, she's laying eggs again. The problem is that she refuses to lay them at the bottom of the cage, so she lays them while on a perch and obviously they fall and break. I wouldn't have a problem constantly cleaning egg mess, but I'm worried she will continue trying to lay eggs until she obtains a full clutch. This will really put her under stress and nutritional deficiencies. Also considering shes not a normal grey, I'm worried about possible defects associated with color mutations and inbreeding that could lead to egg binding. So far, she seems normal. Her droppings are a lighter brown, a little larger and somewhat looser, but I've read that's normal when it comes to egg laying. I've also provided a cuttlebone to keep up her calcium intake.
That bar spacing might be a deterrent that keeps her from coming to the bottom of the cage. Its about half an inch (1.5 centimeters), but whole eggs don't fall through. The birds have no trouble navigating about the cage with this bar spacing; just walking around at the bottom. Additionally, the cage size is 2x2x3 feet.
I don't want to encourage egg-laying, but I do want her to be able to safely produce a full clutch, so later I can try to prevent this from happening in the future. Should a provide a nest box for now? Or something more bare minimum, like a a piece of cardboard to give her a flat surface to sit on?
One final note, I have switched their diet from a free-feed seed diet to a pellet/seed mix about two months ago that is slightly more pellets and is measured out in teaspoons. They eat both the pellets and seeds and I give them fresh veggies when I can (which they love). I was hoping a lower-calorie diet would discourage future egg-laying, but to no avail. I have also removed mirrors from the cage that arouses the male, which might ultimately arouse the female. But would this just encourage him to mate with the female instead?
I would really appreciate any suggestions on how to proceed in this situation.

[Pajarita]

Give her a nest, get fake eggs and replace the real eggs with the fake ones as they are laid (every other day). Stop free-feeding high protein replacing it with gloop and a different fresh green every day in the morning, plus a mix of budgie and cockatiel mix during the breeding season and budgie alone after molt for dinner at sunset. Allow 4 hours of out-of-cage time for flying (hens need to fly to keep the muscles they use for laying in good shape or they can become eggbound). Inbreeding does not lead to eggbinding, it's the lack of calcium that makes the shell too soft to offer any resistance when the hen tries to push the egg out or lack of muscle tone that does it. Give her a dosage of calciboost every time she lays an egg and have a cuttle bone in their cage all the time.

[gmgallen]

Alright, will do. Thanks for the advice and info