I just upgraded to two asus r9 280x. Was having the same issue. Only the two dvi monitors would work. After a few Hours I was able to get eyefinity to work with 2 dvi and 1 hdmi. I have 3 Asus 23" lcd monitors VH238.
First off I am no expert at this, so I will try to explain what I did as easy as I can.
I have eyefinity working with no addapters 2 dvi and 1 hdmi. I looked online for a few hours and found nothing.
Here is what I did to get it to work.
1. Had to toggle from dvi to hdmi on the monitor that is using the hdmi cable. I did this by pushing a button on the front of my monitor. Sounds dumb but that was the big problem. I bet its the same for most. Looking over small details.
2. Now the monitor is up and running. catalyst detects it, but the resolution is off. I think because it is a hdmi connection it is displayed as a hdtv not a monitor. Go to My Digital Flat Panels, Scaling Options. Move to 0% overscan, you will see the image on the monitor adjust. This should fix the one monitorthat is off on resolution.
3. Set main monitor for eyefinity as one of the dvi port monitors.
4. Create eyefinity group.
That is what worked for me.