Laying Box
You have recognized the main problem with a laying bin constantly in with a chameleon. If you water enough to hydrate a chameleon you could very well end up soaking your laying bin!
I have my female cages directly on a laying box full time. This gives them full access to laying sites. This is useful especially with chameleons like quadricornis who may hide that they have eggs to lay.
The benefits of a constantly available laying box are substantial, but those benefits come with some extra responsibilities.
1) Monitor water saturation. I change out my soil/sand mixture when necessary - even with my set-up that has external drainage.
2) Spot clean. In between soil change-outs make sure the poop gets picked up. Unless you are doing a bio-active substrate, you really don't want that much body waste decomposing in the soil the female will be digging in. I admit I don't have any proof how much would or would not cause a problem, but I have yet to decide it is worth seeing how much poop a bin of dirt can handle. (I think we can agree that this one can stand on assumption).
3) Careful with feeders. Certain feeders will burrow and make their homes in the soil. Superworms are first on the list. I have not experienced them eating eggs, but I am not thrilled that critters like that could be around the eggs and get any bright ideas. Once again, I have no proof. I am just OCD when it comes to chameleon eggs.
Bill Strand