Not really advocating this really, especially if you don't want marathon work outs (2hrs+), but if you want to do the competitive lifts a lot
, you could try Sheiko
(356+ squats a month, depending on which cycle).. or the Smolov squat cycle
(408 squats in the first 3 weeks).
And yes, they both work for raw and un-drugged lifters.
As for the 5/3/1.. I quite like the routine, I like the volume of the main lifts, it's not that I don't like squatting, but it's that I don't feel like I'm under-training because of the AMRAP sets, and I like the cycling of intensity. As for the linear increase being slower, you might find that the given "speed" is exceeded by the program if you test your maxes every once in a while, since one of the motivations of the program is that you don't have to operate at your max ability to be able to perform at your max.
I think assistance work becomes very important on this type of program, not as important as if you're doing true max training, but way more important than if you doing "eastern block" powerlifting style training (ie, tons of volume in the competition lifts at lower intensity, and very little, if any, assistance work). Strict form and a moderate pace is important for the assistance work too, I think, since you're not building the movement itself, but the muscles the assistance work is targeting.
EDIT/PS: Korte's 3x3 is another similar eastern block inspired marathon program..