That was a good starting point - actually by using the Planar command you create a large plane that is trimmed by those curves. It is quite similar to the kind of build-large-sheet-then-trim-back method that I showed above.
Wasn't there a script posted a while back that enabled you to highlight "open" edges or something like that?
It made a good tool for checking your surfaces to see if they were closed as you expected - actually I think it was perhaps as simple as turning on points? (Or perhaps selecting certain points?) Don't remember now...