Windows – How to keep the same 4-monitor setup when using Remote Desktop in Windows 7

I'm using Remote Desktop to connect from a Windows 7 Professional client machine to a Windows 7 Enterprise host machine. Both machines have identical quad-monitor setups. I want the Remote Desktop session to open and to display the exact same four monitors with all the windows laid out exactly as they are when I use the host machine locally.

When I try this, it takes the windows on all four monitors and moves them all to the upper-left monitor of the client machine. I can then manually spread the windows out to all four monitors. This is certainly better than when I had Windows 7 Professional on the host machine and it didn't support multi-monitors. mstsc /span would be good, too except that the 3200×2400 total resolution of the monitors exceeds vertically the maximum mstsc screen size of 4096×2048.

If this is not possible using Remote Desktop, I would be willing to use 3rd party software to meet this need. Free software is a bonus. Software that can also remote into my CentOS box with the same feature is a big bonus. Software that can do both at the same time with easy switching would probably get me to open my wallet.

Of course, I'm really more interested in how to get Remote Desktop to work, since we spent a whole day reconfiguring the machine to Windows 7 Enterprise for it.