Agreed, it's not a good idea to encourage her to breed.
If it helps... This is generally what I recommend for egg-laying hens. (X-post)
- Remove Eggs
- Rearrange the cage
- Move the cage to a new location
- Use a cage grate
- Get a new cage/Use a different cage
- 12-14 hours of complete darkness (may require as much as 16 hrs for 2 weeks - or try providing the opposite, as little as 8 hrs of sleep)
- Full Spectrum Lighting/Better Lighting
- Lower the indoor temperature
- Decrease calcium and protein within the diet (if she is on a high calcium & protein diet prior to laying eggs)
- Remove anything that could be taken as a nest
- Remove anything that could be used as nesting material
- Don't allow her in any dark place or enclosed area
- IMPORTANT: save the eggs in the fridge
- If she lays more than 3-4 eggs, put them back in the cage
- Leave the Eggs
- Leave the eggs alone in the cage
- [Optional] Replace with fake eggs (prevent eggs from breaking)
- Increase calcium
- Let hen sit on eggs for 3-4 weeks or until she gets bored of them
- Once done sitting, toss
Generally speaking, there are triggers to hens laying eggs, and if you can remove the triggers, you may be able to stop the egg laying. Triggers can include toys that she can lay in, a plastic base to a cage, nesting material (i.e. cage bedding), a diet high in protein and fat, too much or not enough light, quality of light, etc. All things that should be considered. Removing the triggers to egg laying should be considered *FIRST* before any drastic measures should be taken. You never know, it could be something simple!
It's great that she eats a varied diet, although if she isn't eating much greens, you may want to add pellets into her diet to help round out anything she may be missing. I would say she doesn't need the seed stick or rice cake and feeding grit can be quite controversial. If you feed celery, it's best to feed it finely chopped up. The "strings" in celery don't always get broken down well in their system and can cause digestive problems.