Monitor stuck at half resolution

[Zolcos]

Monitor: HP ZR30w
Motherboard: Gigabyte H87N-WIFI
CPU: an i3 with Intel HD Graphics 4600
No separate GPU

The monitor has DVI and DP inputs. The motherboard has DVI and HDMI outputs. The native resolution of the monitor is 2560x1600.
I first tried connecting DVI and saw that the max resolution I could use was 1280x800. I tried the bios and driver updates Gigabyte provides for the board, ran Intel's driver scan and update program, and installed HP's "driver" for the monitor. Both Windows and the Intel graphics settings app still max out at 1280x800.
I thought maybe it's a limitation of DVI so I used a HDMI to DP adapter (powered/active model by StarTech that claims 4K capability) but it too only goes up to 1280x800.

I read that you can use CustomModeApp to force an arbitrary resolution. I found this program on my computer but when I launch it, the Select Display menu is empty -- no displays are listed at all. If I start to type a number in either custom resolution field, it crashes.

Is there any way I can drive this monitor at 2560x1600 with this particular computer? If not, what part of my setup is the problem?

 

[LTC8K6]

Well, SL DVI is limited to 1920X1200 iirc.

1 x DVI-I port, supporting a maximum resolution of 1920x1200
2 x HDMI ports, supporting a maximum resolution of 4096 x 2160 @ 24 Hz / 2560 x 1600 @ 60 Hz
* Support for HDMI 1.4a version.
Support for up to 3 displays at the same time
* To set up a triple-display configuration, you must connect a D-Sub monitor using a DVI-to-D-Sub adapter.
Maximum shared memory of 1 GB

 

[Zolcos]

Well, SL DVI is limited to 1920X1200 iirc.

Yep. But the HDMI to DP should work, right?

 

[LTC8K6]

I think the adapter won't do the 2560X1600 60hz.

It looks like neither Startech adapter supports that resolution?

http://www.startech.com/AV/Converters/Video/?filter_AVINPUT=HDMI&filter_AVOUTPUT=DisplayPort

 

[Zolcos]

I think the USB powered one on that page is the one I have. If it can do 4K it should be able to do 2K right? I know 2560x1600 isn't specifically listed, but neither is 1280x800 and that's what I'm getting.

If the adapter really is the problem, though, is there another one that would be more likely to work?