Not really. It's not that much of an angle, but I'm sure the slope doesn't help matters any.
I still never get any spillage unless I rip the door open. I can leave the door wide open while I stand there sweeping up the hearth. My chimney isn't super tall, maybe 16' total.
I think it's a Princess thing. Maybe the bigger pipe moving a larger volume of air? Dunno, but I don't see many complaints from King owners.
This is true, I rarely see a King owner talk about smoke spillage, it seems to be the Princess crowd.