Let me ask you something though. I think you're after an out and out goal scorer to play through the middle and stick chances away. While Sanchez is an amazing player, he's not really that total central striker that I think you need.
What do you think would have been a better move in the long run, 50m for a 28 year old Sanchez, or 50m for a 26 year old Lacazette, a regular 30 goal a season striker?
I'm not asking this because we've got Laca and I'm trying to make myself feel better, it's a genuine question as I think Laca would have stuck away quite a few of the chances you had at Brighton today as he has the highest conversion rate in Europe, nearly 20% higher than Sanchez.
I just think maybe you're looking in the wrong direction to solve your goal scoring frailties.