Full maximise (behind the dock)

None of the maximise commands provide proper maximisation to fill the whole screen. When you have Dock not autohidden, then they only go up to the boundary of the dock. When you have Dock hidden they go near the edge of the screen but a few pixels short meaning you can see other apps and the desktop behind them.

First I thought it was because I was using third party apps to maximise. I tested in Sizeup, Moom and BetterTouchTools. But it turns out the native maximisation is broken to begin with. Nothing will let a window automatically maximise to the full screen size, there will always be some pixels left over wherever the Dock is even if you have it hidden and at the smallest size setting.

At first I thought this question was a duplicate and would provide my answer, but alas it doesn't. It is, of course, possible to move the window behind the dock protected pixels then resize it from the opposite side. But this has to be done for every window manually.

Is there any way to make it so that maximise fully maximises across the entire screen?

Bonus points: if anyone can find software that will allow keyboard shortcuts to do a different action moving a window dependant on where it currently is. e.g. in Windows 7 and above you can hit Windows+Left over and over and the window will first maximise half left, then maximise half right on the display to the left of the current display, then to the left of that display and so on. Likewise, Windows+Down will first restore a window, then minimise.