First Turkey Smoke now with Q-View

I think you're cutting yourself short on the bringing time, and probably aren't going to accomplish much, if anything at all. For a bird the size you're preparing I normally brine for 48 hours, then drain, rinse well, and allow to dry for 12 hours.

I know this won't work with you're schedule at this point, but suggest you start brining Friday after you pick up the bird and go at least 24-30 hours.
 

Good luck.

I've seen a number of guides in the past, but the times all over the place. Some say 1 hour per lb., others say 4 hours per lb., and others are in between. Most of those guides don't take into consideration the actual size or mass of the item, just the weight. 

When I've done whole turkeys, they were in the 15-17 lb. range. I found that 48 hours followed by a really good rinse (in and out), and a 12 hour drying period worked best for me. It's your first time and if you're concerned about over brining resulting in too much saltiness, cut it back a bit but I would go no less than 24 hours.

BTW, I no longer do whole turkeys, and I no longer wet brine them. I part the bird out myself, or just buy the parts. I stagger smoke/cook starting with the dark meat and add the light meat later in the cook. I also use a dry "brine" or cure which I find gives much better results.