In case someone arrives here looking for a solution to a similar problem, I managed to solve it by copying DisplaySwitch.exe from a Windows 10 installation to a different location, and using that instead of the inbuilt DisplaySwitch.exe.
My modified AHK config is:
^!1::
; Ctrl+Alt+1 = Display 1
Run, "D:\Software\Display Switch\DisplaySwitch.exe" /internal
return
^!2::
; Ctrl+Alt+2 = Display 2
Run, "D:\Software\Display Switch\DisplaySwitch.exe" /external
return
^!3::
; Ctrl+Alt+3 = Display 1+2
Run, "D:\Software\Display Switch\DisplaySwitch.exe" /extend
return