Wow, thanks for the help everyone. We have a tentative booking for CPH-MCO via ORD in both directions for $972, decent connections with reasonable layovers (the late arrival in MCO is the only inconvenience, but we can live with it).
I'll look at those other options to save a bit more. We're not too comfortable with booking separate tickets because if something happens on one flight and we miss a connection, we're out of luck. I've sat on runways plenty of times (twice in the last three months for one and three hours) to know that anything can go wrong.
Appreciate the help. The ITA site brings up a ton of options!
Susan