I would use TotalSpace 2 more often but I have to set them up again when I purge a computer or when I do changes on one computer has to be repeated on others. I also would like to do the changes offline (Text Editor) as the UI is slow and time consuming.
The app bindings can be modified either in TotalSpaces, or by ctrl-clicking on the icon of the app in the dock, and choosing Options (then assign that app).
The TotalSpaces UI is a bit more convenient usually, but in fact it’s just a wrapper for the apple implementation.
The assignments are stored in ~/Library/Preferences/com.apple.spaces.plist but you can see if you open this file (for example using Xcode) that each assignment is for a specific space id - so copying the file between machines won’t work because the space ids will be different.
Sorry I don’t have a solution for this.