Everything you needed to know about manually overriding incorrectly probed screen resolutions but nobody thought to write down, seemingly:

$ xrandr -q
Screen 0: minimum 320 x 200, current 3600 x 1080, maximum 8192 x 8192
DVI-I-1 connected 1920x1080+0+0 (normal left inverted right x axis y axis) 477mm x 268mm
   1920x1080      60.0*+
   1600x1200      60.0  
   1680x1050      60.0  
   1400x1050      60.0  
   1280x1024      75.0     60.0  
   1440x900       59.9  
   1280x960       60.0  
   1152x864       75.0  
   1024x768       75.1     70.1     60.0  
   832x624        74.6  
   800x600        72.2     75.0     60.3     56.2  
   640x480        72.8     75.0     66.7     60.0  
   720x400        70.1  
DVI-I-2 connected 1680x1050+1920+0 (normal left inverted right x axis y axis) 0mm x 0mm
   1024x768       60.0  
   800x600        60.3     56.2  
   848x480        60.0  
   640x480        59.9  
   1680x1050      60.0*

This output shows what xrandr has detected. In my case, DVI-I-2 wasn’t showing the 1680×1050 resolution I needed. It’s there now because this output is from after I made my modifications.

$ xrandr --addmode DVI-I-2 "1680x1050"

Was all it took.

Sadly, of course, this is all lost on reboot, despite making changes in the System Settings/Display panel and saving them as default – because even though my screen alignment settings were saved in $HOME/.kde/share/config/krandrrc, the mode 1680×1050 isn’t remembered as being valid for my screen.

Because krandrrc contains a config element like this:

[Display]
ApplyOnStartup=true
StartupCommands=xrandr --output "DVI-I-1" --pos 0x0 --mode 1920x1080 --refresh 60\nxrandr --output "DVI-I-2" --pos 1920x0 --mode 1680x1050 --refresh 59.9543

I simply elected to try adding:

xrandr --addmode DVI-I-2 "1680x1050"

To the front end of StartupCommands, like so:

[Display]
ApplyOnStartup=true
StartupCommands=xrandr --addmode DVI-I-2 "1680x1050"\nxrandr --output "DVI-I-1" --pos 0x0 --mode 1920x1080 --refresh 60\nxrandr --output "DVI-I-2" --pos 1920x0 --mode 1680x1050 --refresh 59.9543

On reboot, my screen resolution is correctly set, and my dualhead config works as expected. Now I just need to remember never to change my screen settings again, or be prepared to make that change again.

Some SEO, hopefully:

KDE4 Manual Resolution
KDE4 Override Screen Resolution
KDE4 Incorrect Screen Resolution