The vast majority of the "tips" on rodent control are things people have heard but have never tried themselves. The baking soda thing is one of them. Let me address some specific questions or statements in your post then I will add an old post from a guy named Howard E that used to frequent BYC and was the expert on dealing with rodents.
Rats will happily feed during the day so putting the feed away at night might help a bit the rodents just fill up during the day.
Baking soda as a deterrent is an old wives tale. There is one simple and always effective way to deal with rats, and that is to stop feeding them. They are there for the chicken feed and mice and rats will live within a few dozen feet to a few hundred feet from their main food source. And natural food sources can support only a few rodents that must hustle for food and expose themselves to predators which keeps the numbers down. Humans upset that balance with garbage, animal feed, animal waste that can be eaten, and by providing cover or concealment to the rodents that are not found in nature.
Here is Howard E.'s past post:
"To the OP (and others like them), if you will spend the time, everything you need to know about rats and how to get rid ofthem will be found in the linksbelow......
https://www.backyardchickens.com/threads/rat-control-the-video-series.1337456/
https://www.backyardchickens.com/threads/rat-control-101.1283827/
https://www.backyardchickens.com/threads/rat-proof-feeder-review.1180514/#post-18610285
This last one is a review of a rat proof chicken feeder built and sold by a BYC member, who is a staunch advocate for the plan of getting rid of rats by starving them out. Remove all sources of feed and they will be forced to move on or starve to death. If you are firmly against the use of poison bait blocks......for whatever reason.......then this is one of the best actions you can take. Bulkfood in metal trash cans.....chicken feed in metal rat proof feeders.Can't get to the feed and birds do not spill and waste feed that therats can survive on."
And the short version of Howard's post? Sanitation, exclusion,elimination.
Sanitation, bulk feed in metal cans or barrels with tight fitting lids, a treadle feeder, clean up the avenues of movement so the rodents have no cover to protect them from their natural predators. In my opinion and experience this is the quickest, surest, andcheapest way to solve a rodent problem.
Exclusion, plugging the holes and building a Fort Knox chicken coop and not leaving an opening for free range. Tough to do and expensive but it could work for rats.
Elimination, poison and traps. Problem is that rats are smart and will quickly learn to avoid both traps and poison bait. Were you to clean them out, the lack of sanitation would mean a new population of rodents would move right in. And there is risk to other animals and the natural predatros and no end to the process, keeping fresh bait out. However, if you have done your sanitation work using poison becomes effective as the rats are starving and will likely try the poison bait. Not needed though, they will leave in a few days as long as you are not feeding the rodents with a compost pile or other animal feed. Not all will leave, your area will have a natural carrying capacity for rodents, natural feed, but that natural ability to sustain rodents is quite small and the natural predators keep them in check and under cover as the rodents hustle to find this natural food.
Do a forum search on "rats chickens" and you will find most of the old wives tales exposed and read of long epic battles against the rodents. Sanitation, exclusion, or elimination all have associated costs but you are already paying for the feed and will recover the initial costs quickly with the first method.
Good luck and remember, it isn't just the stolen feed, disease and predators come with rodents.