Just for discussing this patch improvements,findings and updates.

DOWNLOAD LINK @ PCGW

GOG compatible settings:

[Log]
# Enable to print debug info from Silent_Hill_4_PC_Fix.dll to a console
LogToConsole = 0

[GameWindow]
# Set resolution width
ScreenWidth = 1920

# Set resolution height
ScreenHeight = 1080

[SilentHill4]
#Use HKEY_CURRENT_USER instead of HKEY_LOCAL_MACHINE
RedirectRegFunctions = 1

# Patch FOV
PatchFOVAndEnableControl = 0

# Vertical FOV value, leave at 0 to use automatic detection. Default is 0.78
VerFOV = 0

# Horizontal FOV value, leave at 0 to use automatic detection. Default is 1.0
HorFOV = 0

# Increase the resolution of background screens
IncreaseBackgroundResolution = 1

# The map will zoom in correctly to your aspect ratio
FixMapZoom = 1

# Disable system check
DisableSystemCheck = 1

# Disable Safe mode
DisableSafeMode = 1

# Disable cutscene borders
DisableCutsceneBorders = 1

# Fix the FPS in cutscenes
FPSFix = 1

# Modify the blur effect, leaving these at 0 is recommended
# Default is -3.0
Blur1 = 0

# Default is -2.0
Blur2 = 0

# Default is -4.0
Blur3 = 0

# Default is -6.0
Blur4 = 0

# Set the sensitivity, hotkeys are page up and page down (The value set here is used at start)
# Default is 0.06666667
Sensitivity = 0.06666667

# Hotkeys to invert X axis is F3 and Y axis is F4


EDIT:


# Increase the resolution of background screens
IncreaseBackgroundResolution = 1

Having this option enabled will make your pause menu to focus on a squared section of the screen, by disabling this option (with a 0) the pause menu issue will be fixed.

I'm not finding a workaround for menus not to be stretched and to mantain the 4:3 AR, considering the game uses both dxcfg.exe and the internal graphics option it MAY be solved by playing with those values.