Wirelessly posted (BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
"Is it possible to somehow book the direct Iberia flights and pay using my BA miles?"
Yes, but you will still pay a small fortune in BA's fuel surcharges for flying IB TATL. To book the IB flights at ba.com, you have to keep searching until you find a date when there are no BA award flights offered on the route; then, exercise the option to search partner airlines, and then go forward or back to the date when you actually want to travel.
The alternative is to phone BAEC, and be prepared to pay the telephone-booking fee.