Kirk - it may not be a Mavericks issue as I have had the same or similar issue in Mountain Lion since I upgraded my graphics card [to an Apple one] in my MacPro. It takes ages for the screens to get their act together and then when it finishes turning on and off, all windows from all programmes are on my left monitor, which is where I have menu bar. I can't recall if it happens when I'm I booted up into my Mavericks setup as I've not committed to Mavericks yet and due to this glitch when I wake up machine I usually do something else whilst if faffs about getting its act together.
[I don't tend to commit a new Mac OS for work until update 3 or 4. Too many bugs otherwise].
The multi-monitor improvements in Mavericks over previous versions are OSX swapped a crappy system for a differently crappy system. I could do better multi-monitor setups in Windows 15 years ago, so I hope the latest update helps to make amends.
A few times I've 'lost' programmes in OSX as when you Cmd+Tab between them they vanish if in full screen mode and can only be seen again if you use Exposé
At least your second monitor is actually working as that appears to be a 10.9.2 glitch