#340-345 is doing this, and he thinks he's adding #60ish pounds to it in a week.
He mimes 365 pounds.
Also, he is doing a high bar squat, so he can lower it and it'll be easier. Not sure if you can do a lower bar squat with the lame squat aid, though.
He isn't wearing a belt and putting on a belt helps a lot at the bottom, so it'll be easier.
All in all, 405 is possible. If I was him, I'd probably just keep building the 365s though. Rushing to 405 is only going to end in one of two things: very very sketchy 405 or injury and appeasing the haters.
Brian: I'd do pause squats. Lower weight, just sit at the bottom. You'll get a lot of stability improvement.