If you're going to be digging around in the deep litter in your run, you would be wise to wear a mask to filter out any aspergillus mold spores that may become air-born. If you encounter any black molds, those are likely aspergillus molds. You can kill these spore with a bleach/water solution.
It's a good plan to kick the chickens out to free range while you work on the run. Turning over the material and letting it get mixed with oxygen and dry out will neutralize botulism toxins.
You know what to look for with the rat poison. Depending on how toxic the formula is will determine how thorough you need to be trying to find it all. If you have tunneling under the surface, you've got a problem. Rats carry disease in their droppings as well as fleas.
I would be tempted to move the run and make the new one with hardware cloth barriers so the rats can't tunnel in. Or, if you want a very effective weight loss program, remove the sub-floor of the old run, taking out all the rat droppings and nesting material, spray well with a bleach solution, then install hardware cloth barriers.