Broody hens can and sometimes do return to the wrong nest after their trip to the break room. And, it's not at all uncommon for several hens to crowd into the same nest box to lay an egg, even in a small nest box. More often, hens will wait until your broody gets up for a break, then they'll go into her nest and add their eggs to her already developing clutch. That's why it's recommended that the broody be kept with the flock, but her nest be inaccessible to the rest of the layers. A dog crate would be an ideal situation if you have the room.
Do you have access to an incubator? Any experience hatching with an incubator? If I were you, I'd locate an incubator. Just as soon as I had a broody, I'd start saving eggs to hatch from my own flock. I'd fire up the incubator, and order those eggs. Then, I'd split the OEG eggs between the broody and the bator, so that there was a mixture of OEG and eggs from the flock to set in the bator and under the hen at the same time. You'll need to be sure she doesn't have eggs under her that have already started to develop when you set the new eggs. Then, when the eggs hatch, depending on the hatch rate, you can slip the chicks from the bator into the nest with the broody, and let her raise them all.