Well I tried calling back again and once again no joy. But I had to book my ticket by today for other reasons, so instead of going VFA to ZRH I'm going to VIE, treating it as a stopover and then returning from VIE. Not as nice as ZRH first but they're so close I can make due.

Another interesting tidbit, the flight out was going through YZZ (Toronto) on Air Canada. Apparently that is treated as a domestic carrier or something and the layover couldn't be more than 4 hours. So what was originally a 6 hour layover there was too long, but we worked it out.

Thanks for all the help y'all.