Thanks for so many useful replies so quickly.
I'll brace myself to ring the ICC and I now feel much better informed to respond to what they've got. I want to go for two weeks but, within a week or so, I can move my dates around to accommodate what they have. Not being able to see LX on the ANA tool complicates things a bit.
The advice about the tax ex-Argentina is also useful as I would, as usual, have gone for two one ways (and reeled in horror by the sounds of it at the cost).
Haven't been to BA before but am looking forward to it. Not planning to travel extensively - just BA and a couple of short hops to Iguazu Falls and Uruguay.