In my initial post I described what I know how to do. In particular it is possible to set things up so that you have 2 copies of X running, one for each monitor. Now each one can have independent sets of virtual desktops.

I believe that some window managers have even figured out how to enable cut and paste between the copies of X, though I'm not entirely positive on that. If they haven't, though, the flexibility is more important to me than cut and paste. Worst comes to worse, I can save data to a file on one monitor, read it on the other.

The gap between this and what I really want is that 2 copies of X ties the virtual desktop to the monitor, which means that I can only get some combinations of virtual desktops.

Now 3 of my desktops are my email, my browser (which has request tickets), and one in which I'm trying to develop and run a long one-off report that occasionally needs nudges. While looking at the report I might need to be referring to an email or to the request ticket. While replying in email I might need to be looking at the report I'm developing or a request ticket. While entering stuff in the request ticket I might need to be looking at email or at the report. So I really might wind up working in any of the desktops and referring to stuff in either of the other two.

So tying the virtual desktop to the monitor means deciding which combination I can't display.

However, as my response to bepatient pointed out, getting what I want requires a ton of support from the window manager. And it doesn't look like any window managers supply that support.

Cheers,
Ben