I had a similar (not identical) problem to yours and managed to find a solution. Maybe it will be helpful to someone anyway.
I assume that you've got the two monitors working and that the single desktop is extended across both (i.e. such that you can drag apps onto the second monitor).
Right clicking on the GNOME panel at the top or bottom of the screen gives the option of 'New Panel'. Click this and drag the new panel onto the second monitor.
Now right click on the new panel and select 'Add to panel'. Scroll down to the bottom of the resulting list and select 'Window List'.
Now you have a list of windows on your second monitor. The new window list will only show the windows which are sitting on the extended part of the desktop, while the window list on your main monitor will similarly only show windows residing there.
All these windows are running in the same workspace, but this technique 'approximates' the one-workspace-per-monitor that you originally asked for. With this setup you can easily drag windows from one monitor to the other and, naturally, copying/pasting works properly too.