Air Canada have the same non-refundable, non-changeable, non-cheap fares, but I also understand that that isn't as bad as it sounds.
If you want to change the ticket it costs, and if you want to cancel you don't get a refund, BUT I believe they will offer you a credit note (to be used in the a year or so), in the absence of the cash. Maybe you could get the same from UA and, perhaps even use it with another Star Alliance partner (whichever scheme UA are signed up to)
Just a thought, but worth a try
