We had the same problem booking IC flights earlier this year - in fact the lowest fares we could find were via IC's website (much cheaper even than what our TA could do and we have a really good one).
In the end we simply called the IC GSA in Australia and the ticketing was done over the phone (even for an 'internet fare') and we got our tickets the next day. Couldn't have been easier.
Looks like IC has GSAs in most countries (details via their website).
Regards
LME ff etc etc