cannot set 4k resolution on external monitor with lower refresh rate

Question

I have a new 4k monitor that's capable for 3840x2160 at 60hz. Unfortunately I only have HDMI, which means that the best I can hope for is running at 30hz (my understanding). If I try to switch the resolution using Display Manager to 3840x2160, the external display just goes blank.

I've tried several things with xrandr. The first was just

% xrandr --output DP-1 --mode 3840x2160 -r 30.00

(I've also tried every other display rate the xrandr shows as available---see below.)

This causes the screen to blink, but then return to 1920x1080 (the default that works fine at 60hz).

I've also tried creating new modes:

% gtf 3840 2160 30
  # 3840x2160 @ 30.00 Hz (GTF) hsync: 65.91 kHz; pclk: 339.57 MHz
  Modeline "3840x2160_30.00"  339.57  3840 4080 4496 5152  2160 2161 2164 2197  -HSync +Vsync
% xrandr --newmode testmode 339.57  3840 4080 4496 5152  2160 2161 2164 2197  -HSync +Vsync
% xrandr --addmode DP-1 testmode
% xrandr --output DP-1 --mode testmode

This actually causes something to happen. Both the laptop screen and the external monitor turn blocky and orange and striated for about five seconds, and then it returns to the previous settings.

If I look at the end of /var/log/syslog right after that, it shows:

Apr  1 18:50:40 hal-blade kernel: [ 2682.254996] [drm:intel_dp_link_training_clock_recovery [i915_bpo]] *ERROR* failed to enable link training
Apr  1 18:50:40 hal-blade kernel: [ 2682.263677] [drm:intel_dp_start_link_train [i915_bpo]] *ERROR* failed to start channel equalization
Apr  1 18:50:40 hal-blade kernel: [ 2682.355692] [drm:intel_cpu_fifo_underrun_irq_handler [i915_bpo]] *ERROR* CPU pipe B FIFO underrun
Apr  1 18:50:40 hal-blade kernel: [ 2682.360121] [drm:intel_dp_link_training_clock_recovery [i915_bpo]] *ERROR* too many voltage retries, give up
Apr  1 18:50:40 hal-blade kernel: [ 2682.367507] [drm:intel_dp_link_training_clock_recovery [i915_bpo]] *ERROR* too many voltage retries, give up
Apr  1 18:50:40 hal-blade kernel: [ 2682.374924] [drm:intel_dp_link_training_clock_recovery [i915_bpo]] *ERROR* too many voltage retries, give up
Apr  1 18:50:40 hal-blade kernel: [ 2682.382413] [drm:intel_dp_link_training_clock_recovery [i915_bpo]] *ERROR* too many voltage retries, give up

Lastly, here are some outputs in case they're helpful:

% xrandr --verbose
... (skipping part about built in display) ...
DP-1 connected primary 1920x1080+0+0 (0x79) normal (normal left inverted right x axis y axis) 600mm x 340mm
    Identifier: 0x43
    Timestamp:  22921
    Subpixel:   unknown
    Gamma:      1.0:1.0:1.0
    Brightness: 1.0
    Clones:     HDMI-1
    CRTC:       0
    CRTCs:      0 1 2
    Transform:  1.000000 0.000000 0.000000
                0.000000 1.000000 0.000000
                0.000000 0.000000 1.000000
               filter: 
    EDID: 
        00ffffffffffff001e6d085b766d0000
        021b0103803c2278ea3035a7554ea326
        0f50542108007140818081c0a9c0d1c0
        81000101010104740030f2705a80b058
        8a0058542100001e565e00a0a0a02950
        3020350058542100001a000000fd0038
        3d1e871e000a202020202020000000fc
        004c4720556c7472612048440a2001a7
        02031d7146902205040301230907076d
        030c001000b83c200060010203023a80
        1871382d40582c450058542100001e00
        0000ff003730324e54524c3055303232
        0a000000000000000000000000000000
        00000000000000000000000000000000
        00000000000000000000000000000000
        0000000000000000000000000000008f
    Broadcast RGB: Automatic 
        supported: Automatic, Full, Limited 16:235
    audio: auto 
        supported: force-dvi, off, auto, on
  3840x2160 (0x73) 297.000MHz +HSync +VSync +preferred
        h: width  3840 start 4016 end 4104 total 4400 skew    0 clock  67.50KHz
        v: height 2160 start 2168 end 2178 total 2250           clock  30.00Hz
  3840x2160 (0x74) 297.000MHz +HSync +VSync
        h: width  3840 start 4896 end 4984 total 5280 skew    0 clock  56.25KHz
        v: height 2160 start 2168 end 2178 total 2250           clock  25.00Hz
  3840x2160 (0x75) 297.000MHz +HSync +VSync
        h: width  3840 start 5116 end 5204 total 5500 skew    0 clock  54.00KHz
        v: height 2160 start 2168 end 2178 total 2250           clock  24.00Hz
  3840x2160 (0x76) 296.703MHz +HSync +VSync
        h: width  3840 start 4016 end 4104 total 4400 skew    0 clock  67.43KHz
        v: height 2160 start 2168 end 2178 total 2250           clock  29.97Hz
  3840x2160 (0x77) 296.703MHz +HSync +VSync
        h: width  3840 start 5116 end 5204 total 5500 skew    0 clock  53.95KHz
        v: height 2160 start 2168 end 2178 total 2250           clock  23.98Hz
... (skipping lower resolution items) ...
HDMI-1 disconnected (normal left inverted right x axis y axis)
    Identifier: 0x44
    Timestamp:  22921
    Subpixel:   unknown
    Clones:     DP-1
    CRTCs:      0 1 2
    Transform:  1.000000 0.000000 0.000000
                0.000000 1.000000 0.000000
                0.000000 0.000000 1.000000
               filter: 
    aspect ratio: Automatic 
        supported: Automatic, 4:3, 16:9
    Broadcast RGB: Automatic 
        supported: Automatic, Full, Limited 16:235
    audio: auto 
        supported: force-dvi, off, auto, on

(Note: I'm not entirely sure what the deal is with DP-1/HDMI-1. There is only an HDMI port on the machine. There is also DP-2 and HDMI-2.)

% lspci | grep VGA
00:02.0 VGA compatible controller: Intel Corporation Device 5916 (rev 02)

I'm not sure what else is helpful... This is on Ubuntu 16.04.2 LTS xenial, on kernel 4.4.0-71-generic.

Thanks!