If you're crossfiring, only the ports on card 1 are active, all ports on card 2 are disabled. If you disable crossfire, the ports on card 2 can be used, but you can't use Eyefinity or use the GPU grunt of both cards on one game.
HDMI, DVI and VGA each require a clock signal, Displayport does not. 5xxx - 7xxx series AMD cards can only produce 2 clock signals. Using a passive connector, such as your DP-HDMI cable, will force the card to send a clock signal through the cable, which is why you can only get 2 screens to work at once. You need an Active Displayport to HDMI adapter, as this produces the clock signal so the GPU itself doesn't have to.
FLEX models of 5xxx-7xxx series cards have 3 clock generators, and the new R9 290 and 290X can support 3 screens on DVI/HDMI, but your 280X is a rebranded 7970, so you WILL need an active adapter to run your 3rd screen. Something like Startech's DP2HDS would be perfect, but pricey. Would be cheaper to go Active DP to DVI, then use a DVI to HDMI cable, but can't guarantee that'll work.
