Windows Live Mesh has a remote connections feature, similar to Remote Desktop, which can be accessed from the Windows Live Mesh client and the Windows Live Devices website. I've used it frequently when I needed to access my home machine from work - it connects despite no ports being forwarded in the router and it doesn't mess up my multi-monitor configuration at home (normal Remote Desktop will change the resolutions and such).
That was until I changed my multi-monitor configuration at home.
Old arrangement: 1280x1024 / 1600x1200* / 1280x1024 (* primary)
New arrangement: 1280x1024 / 2560x1440* / 1600x1200 (* primary)
Then, every time Windows started, shortly after the login screen appeared, all the monitors would jumble themselves up in to something very closely resembling the old arrangement: 1280x1024 / 1280x1024 / 1600x1200* (* primary). It seemed clear something was attempting to put the monitors into the old arrangement based on some saved information, but it wasn't obvious what that something was.
To diagnose the issue, I carefully timed when the monitors first started showing signs of rearrangement after boot and consulted the list of processes and their start times (from "wmic process") to see what was starting at or just before the rearrangement.
That's when I spotted "C:\Program Files\Windows Live\Mesh\wlcrasvc.exe", the Windows Live Mesh remote connections service, starting just seconds before the rearrangement.
So up came Registry Editor (regedit.exe) and a look through HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft until I found HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Live Mesh. Hiding under there, at HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Live Mesh\Remote Desktop\DisplayDevices, is a key for each display device on the machine and some monitor arrangement data (x, y, width, height).
I stopped the Windows Live Mesh remote connections service and deleted the entire HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Live Mesh key, since it didn't appear to contain anything except the display devices information. Upon restarting the service, some parts of the key came back but no monitors got rearranged and, upon connecting from another machine, the display devices keys came back, but with my new arrangement. I restarted the service again to be sure, and nothing rearranged itself.
Fixed!