Originally Posted by
apuleius
the flights are shown as wide open on the Continental availability rewards booking website.
They were not "wide open" when I checked their a few minutes ago. I can see limited availability with CO and AC on 3 January LHR-EWR-YYZ-SJO, including seven hours at EWR, or with CO and US on the same date LHR-EWR-CLT-SJO. In both cases you'd be travelling for 24 hours plus whatever time you need to get to and from the airports.
Is there any particular reason for wanting to go via Houston or New York? If not, don't limit your search unnecessarily. I can't see any LHR-YYZ availability on AC right now, but that would be a nice option. Alternatively, consider starting with a short hop to mainland Europe and letting someone else take you across the Atlantic. Usually plenty of C (business) availability with LH, including around your dates.