If you don't mind cheating a little, sodium phosphate is a game changer. If you order now, it might get to you before Wednesday.
http://www.butcher-packer.com/index.php?main_page=product_info&cPath=2_215&products_id=760For brining: Use it at about 1.0% of the weight of the water. So if you have a 15 lb bird, 2-3 gallons of water, use 0.25 lb of sodium phosphate in addition to your salt, sugar, and other ingredients.
Make sure and dissolve it in the water first, then dissolve the salt and sugar. Otherwise, you will be stirring for a while.
Also, I don't really care for the idea of dissolving the ingredients in hot water and then cooling them down. In some
rare cases, the ingredients can "come out" of the solution when it is chilled down quickly. You should normally have no issue getting everything dissolved in either tap or cold water; you just might have to spend a little more time mixing real well.
Edit to adjust the formulation