Okay, I totally appreciate your position and I respect you beliefs.
I won't try to sway you on that but I will tell you, the best thing for you and for your birds will be to prevent hatching. That is not going to mean you will be destroying the eggs. Quite the contrary. You will be doing everything possible to prevent them being actually damaged. You are catching this early on and that's great. Even if they are fertile, they are no more and no less, at this moment, any different from the chicken eggs you buy at the store to eat yourself. It's also great that you seem to have them on a pretty good diet and I'm very relieved she has a cuttle bone available. No matter what, don't ever let her run out of it. It is a critical source of calcium for them both but it can literally be life or death for a female when she decides to lay. Without a huge reserve of calcium in her system, she will not be able to form firm shells for her eggs. Each egg puts a big draw on that calcium. If she should run low, her body will first rob in from her bones. That of course leaves her at great risk of a broken bone. Then when that runs out, the shells are too soft, she cannot pass them and will be egg bound.
That is a life threatening emergency so you want to take all possible steps to avoid that. She needs a safe place to keep her eggs safe and undamaged but you do not want anything remotely similar to a nest box. That is too dark and private and is another stimulus for laying. I suggest one of the clear plastic, shoe box size storage boxes.
Put it on the cage floor, line it with a thick layer of paper towels, leave the lid totally off and put her eggs in it. But, since we are assuming they are fertile, there is one step you take first. This is how you prevent them from ever hatching. Don't do them all at once. Take two, very gently bring them to just short of a boil, cool back down to the slightly warm temperature they keep them, put a tiny dot on the end of the egg with a felt tip or Sharpie pen and return them, putting them in the clear box. Then heat up the remaining egg and any that follow, the same way. What this does is prevent a chick from ever forming in the egg. Let her tend them for as long as she wants. Gestation is 19-21 days. She might sit them that long, longer, or less. There is no way to predict when she/they will give up on them. If you have seen her ignore them for at least 3 days, then it should be safe to dispose of them. If the eggs get damaged, you will have to pitch them because they will grow bacteria. This step of almost hard boiling them should also make them more sturdy. But, if they get damaged in spite of your best efforts, it's a good idea to have suitable fakes on hand. Here is a web site where you can get some. Click here: Fake Eggs, Artificial Eggs, Plastic Bird Eggs stop laying. You might be able to find some that will fool her at a craft store but I know these from this site are perfect replicas. You can also use the fakes to help slow her down. The next time she lays one egg, add two fakes to her "nest". Be sure she is getting as many vegetables, leafy greens, (not spinach and no ice berg lettuce) as possible. She can also have hard boiled or scrambled eggs, cooked brown rice, well done bean mixes, squares of toasted whole grain bread and many other people foods. For the future, there are ways to discourage laying.
The pet store person was partly right in that adding a nest box, or allowing them access to anything dark and private can inspire laying but as you have seen, not having one will not change her mind if she is determined. Other steps you can take to discouraging future laying is doing things that upset their routine for a while. When that happens, often they will think this is not a good situation for raising a family and she may not lay. Moving the cage to different locations is good, if only across the room for a few days, then back. Rearranging things inside the cage is good. Another very important step is to restrict them to no more than 10 hours of "daylight". Do that by using a very dark cage cover. Cover earlier in the evening or uncover later in the mornings, whatever fits your schedule the best. It's the increasing daylight hours of spring and summer that is a prime trigger for laying.
If you need more help with the diet just let me know. I hope these suggestions will help you out and will be options that will let you approach it with a clear conscience as well but I'll be here if you have any further questions about any of it.
Best of luck with your decision and with what you decide to do.