You haven't provided model or known modes supported of either your display or
your CPU, or your cable connection type you're using or have tried to use, or
what mode you actually want to use. These limit what help you might be able to
get from any mailing list.
Please provide a reference that states my card is supported by it, as well.
Full specifications for the R9 270X seem to be a secret. I searched the web
without finding out what specific modes it is supposed to support.
e.g. https://us.msi.com/Graphics-card/R9-270X-GAMING-2G.html#hero-specification
suggests it ought not be the limitation, but lists no modes at all.
http://xfxforce.com/en-us/products/amd-radeon-r9-200-series/amd-radeon-r9-270x-double-dissipation-edition-r9-270x-cdfc
says maximum resolution via Dual-link DVI is 2560x1600. That's less than 4K, so
you can't use that cable type to get 4K. With the right DisplayPort or HDMI
cable, you should be able to get 4K, but cables don't always live up to claimed
specifications.
I don't have your hardware, so can't guarantee anything.
I am indeed using a Displayport cable; my HDMI cables don't work at 4K. In Wheezy I had 4K using either the Radeon or the integrated graphics. In Jessie I can only use the integrated graphics. The fglrx driver is incompatible (with Gnome3 apparently, but it must be all aspects of Gnome3 as I use xfce with the gdm). As I mentioned before, blank screen. It apparently boots, but nothing ever displays, using the radeon driver. I am waiting patiently to see what Stretch brings in this area.
You did not mention whether the driver you recommend provides 4K support, or a reference confirming it supports my card.