I second or third or fourth the suggestion of scrounging some points to go for CX F! The marginal cost is small compared to the marginal benefit.

And, not to sound like a shill as I have nothing to gain, but have you considered working with one of the award booking services? They will check all gateways and get creative with routing. That plus the fact that they do the phone booking might save you a lot of trouble for what I think is a relatively small fee (I have used one of the services myself).