People overthink this so much and impose restrictions that don't exist. Broody hens can raise chicks if the temperature is over 90 F every day, they can raise chicks if there is snow on the ground. They don't worry about how much cooler it has to be or about it dropping 5 degrees a week. There is no reason to make this that complicated.
What you need is one spot warm enough in the coolest of conditions and a spot cool enough in the warmest conditions. What is warm enough? If you were using some type of area heater like a radiator or heat lamp your chicks will tell you. If they are cold they get as close to the heat source as can. If they are hot they get as far from it as they can. If they are scattered or some are going back and forth they are fine. If the heated area is too hot they don't go in to stay very long. It can be too hot as long as they are not trapped there.
How cool is cool enough? Anywhere from freezing to probably 85 F. Chickens are not going to overheat at 85 F. They should be OK at 90 F but leave yourself a bit of a cushion. The risk of overheating is when the brooder is so small that your heating device raises the temperature throughout the brooder to a dangerous level. That's why I don't like heat lamps if you are using a small aquarium or bin, those are easy to overheat.
We purchased a brooder plate, but what I can't seem to find much info on is what the room temperature should be.
You can't find that information because with a heat plate it isn't that important as long as it is within the capabilities of the plate keeping them warm. Some manufacturers set that as a 50 F minimum, some don't mention it. Either of the three areas you mentioned would work. One thing I'd watch, you don't want a breeze hitting them, wind chill can be a problem. I don't recall anyone else mentioning that.
we don't want that kind of mess in the house. But maybe we don't want it on our freezers etc in our utility shed.
You might consider covering your freezers etc with old sheets.
I did not see where you mentioned where you are located. Most chicks can be in the coop without additional heat by the time they are 5 weeks old. But that will depend on your climate wherever you are.
The pet owner in me wants to see them when they are little and get to know them and be able to observe their behavior to make sure they are ok.
The entertainment and educational value of watching them is immense. They are easier to tame if you can be with them at a young age. Those "mess" comments about the dust are real though. Hopefully you can put on a coat and sit with them.
Where are my manners, welcome to the forum from Louisiana. Glad you joined.