At this point, it seems to be you are well informed and up to speed on your options. But as for your hope that you may only have a small captive bunch left, don't count on that. A rat that dives through your toilet may be using that to come and go and if he is, others are too.
But that also begs the question......go where? Even if he is using a septic line / sewer pipe as his personal highway, where does that pipe go? Some older homes don't have a private septic treatment system (septic tank or lagoon). Some only have a hot line to some remote ditch. If so, your rat boy could be walking up that. Or perhaps going in and out of some vent pipe or clean out riser?
In addition to all else, you need to be hunting for their harborage. Where they live. Even if not in or under your house, they are somewhere near it. When the door was left open, they came from somewhere.
So while prepping for battle, do work to find and eliminate all entry points. Clean up access to any pet food, chicken feed or anything else they may be eating, and find out where they live. Do the last bit for certain.
And lastly, I would urge you to keep an open mind on the rat baits. When properly used, they pose little risk to pets, and time and time again, after all else has been tried, they have been proven to be the only thing that really works.