Why not water thaw while still in the wrapping prior to brining? As long as the water you use to thaw is between 33 and 39 degrees it would still be safe to brine for a couple of days before cooking.
Whatever you brine in, full it with cold water and use a probe therm to check temp. If it's 40 or above just refrigerate until below 40, such the bird in still in the wrapping, and stick the brining container in the fridge to keep the water under 40. Thaw time will be accelerated.
If you can't fit your brining container in the fridge, just keep the probe therm in the water while thawing. One you start to flirt with 40, stick the bird back in the fridge and switch the water out for colder, then return the bird to the water. Just make sure the bird is completely submerged the whole time, just like with brining.