God forbid Copa's call center agents actually add value to their company's operations. That would be sacrilege! Most would likely want to get you off the call so they can get to their 15th smoke / coffee / whatever other break.

Yes unfortunately at this time your only option is to use an Expedia or some other OTA if you specifically want those 12+ hour connections. In fact Booking.com actually automatically offers it as the best through connection if you do a multi-city search.