I can use a 1600W power supply, but I fear this may be oversaturated too (but I'm open to underclocking the CPUs)
1600W power supply would be only enough for 2x6990s. It would be a waste to use three of them and underclock so much. It be much better to get extra power supply and use it for the third 6990. That way you can get the full potential from all the GPUs.
600-700W per 6990? That's completely incorrect. Even when OC'd there is absolutely no way a 6990 is sucking back that much. As I've stated I have an actual watt-meter attached to my system all day every day and even when clocked @ 940/1250 the 6990 isn't using more than 400W at 100% load. I double-checked this by shutting down each core and bringing them back up again. (Revising my advice here: if you are OCing the cards then AX1200 is probably too little).
That said, there is something in what Dairoux is saying. Often large PSU's are sold at a premium. There's nothing wrong with using multiple small PSU's except for the space, mess and inconvenience of powering on something that isn't attached to your mobo. Estonia has this mobile rack machine they use for folding which they built on the cheap. Each 4U rack unit had 4x GTX 295 and instead of using a single large PSU they used multiple 850W units. You could do the same. Look for something Gold or Platinum rated. Also if you have a 220V line or can have one installed. The PSU will be even more efficient.