Why don't I have a custom title by now?!
That's because it'll assume the image stretching will be done by the monitor (pixels will not be square).
So, what I found is, PrBoom+ will do the aspect ratio correction, only if you choose the correct resolution to match it. For example, PrBoom+ will only correct the aspect ratio if you choose the right resolution to match the aspect ratio. Like 640x480 with 4:3, or 1280x800 with 16:10. If you choose a 4:3 resolution with a 16:10 aspect ratio, or vice versa, the aspect ratio will not be corrected.
Suppose you run Doom in 640x400 (logical 16:10) on a 4:3 screen, and pixels are stretched by the monitor to be 20% taller than they are wide. If the port also stretches them to perform aspect ratio correction, they'll end up being hypercorrected -- that is to say, wrong but the other way around.
Now as for fake contrast -- you're pursuing a red herring. PrBoom+ does fake contrast in exactly the same way as vanilla Doom, Chocolate Doom, or any other Doom port. The difference isn't in fake contrast handling. Fake contrast is nothing more than increasing or decreasing a value, it'll be decreased or increased in the same way and to the same values in every Doom port out there -- even the fancy-schmancy OpenGL ones.
The difference is in rendering the result. The vanilla software renderer is extremely dependent on screen size and resolution, to the point that light levels can and will change if you reduce the screen size into a small window (remember the effect of the +/- keys?).
Which brings up the next point:
I'm not convinced. If your screen is CRT, it should stretch the image to fit itself, resulting in a physical aspect ratio correction done by the hardware. In windowed mode however, if the desktop resolution gives you square pixels, aspect ratio correction should be done in software by the port. Therefore: use 4:3 window sizes, multiples of 320x240.
Regardless of if I'm in window or fullscreen mode, it doesn't have an effect on whether it stretches or not. The results are the same.
Looking at your first pics, I see aspect ratio correction done by PrBoom+.