I've always had this exact same problem. Three monitors - when I change one of them, DesktopCorral always starts on the leftmost monitor, no matter where I put it on the center monitor.
In the settings file, there is Dock > CurrentMonitorId = 0
There is also Settings > LastMonitorId = 0
Jesse, what does that setting mean? Usually, monitors are numbered 1,2,3.
On a hunch, I changed those values to 1, quit DC and restarted it, and it now starts on the center monitor.
I think that whatever triggers DC to reallize which monitor it is moved to - well, it's either broken somehow or it doesn't save the value. OR, when you unplug a monitor, which causes all windows to move to another monitor, DC changes it's monitor ID or gets it wrong. When you plug the other monitor back in, you have to manually drag DC back to it's right place - but now the IDs are wrong - OR when the other monitor is plugged in, DC doesn't know it and so doesn't update the monitorID in its settings.