During the winter (since you are in MN), you probably don't need to keep it in the fridge. If you boil the brine in only 1/3 of the liquid and use ice cubes for the rest of the volume you start with a safe cold temp and some is ice. [

You might check for a nearby restaurant supply store. They have relatively inexpensive food grade plastic buckets with lids. It's easier to brine a turkey in something that's more tall than wide.]

Or you could use a smaller igloo cooler (which can be cleaned with bleach water before and after). Same Ice to brine method and again you can hold it at an ice cold temp safely for long enough to finish brining process.

Thanks! That's the answer I was looking for.

I'd do the garbage bag -- much easier. Also then you don't have to worry about the liquid sloshing around and potentially spilling.