Black screen of death then unresponsive Docker daemon after reboot

While running a bunch of containers, and suddenly OS X panicked (showed that black error screen). After rebooting, Docker is no longer responsive (all commands time out).

This is what syslog reports right before the crash:

Jun 23 16:07:06 xikinbook iTerm2[657]: Time to encode state for window <PseudoTerminal: 0x7f8122428600 tabs=6 window=<PTYWindow: 0x7f812262df30 frame=NSRect:
{{0, 0}, {1280, 800}} title=docker-compose alpha=1.000000 isMain=1 isKey=1 isVisible=1 delegate=0x7f8122428600>>: 0.01208996772766113
Jun 23 16:07:19 xikinbook CalendarAgent[513]: [com.apple.calendar.store.log.caldav.coredav] [Refusing to parse response to PROPPATCH because of content-type:
[text/html; charset=UTF-8].]
Jun 23 16:07:19 xikinbook Screenhero[537]: JS Log: Strophe (1): _dataRecv called
Jun 23 16:07:20 xikinbook CalendarAgent[513]: [com.apple.calendar.store.log.caldav.coredav] [Refusing to parse response to PROPPATCH because of content-type:
[text/html; charset=UTF-8].]
Jun 23 16:07:29 xikinbook Docker[1293]: TCP 54.231.12.184:443 > 192.168.65.2:41879 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:29 xikinbook Docker[1293]: TCP 54.231.49.164:443 > 192.168.65.2:45830 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:30 xikinbook Docker[1293]: TCP 54.231.49.164:443 > 192.168.65.2:45852 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:30 xikinbook Docker[1293]: TCP 54.231.49.164:443 > 192.168.65.2:45848 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:31 xikinbook Docker[1293]: TCP 54.231.49.164:443 > 192.168.65.2:45850 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:32 xikinbook Docker[1293]: TCP 54.231.49.164:443 > 192.168.65.2:45858 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:32 xikinbook Docker[1293]: TCP 54.231.8.136:443 > 192.168.65.2:43044 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:33 xikinbook kernel[0]: ip4_output (ipsec): error code 22
Jun 23 16:07:33 xikinbook iTerm2[657]: Time to encode state for window <PseudoTerminal: 0x7f8122428600 tabs=6 window=<PTYWindow: 0x7f812262df30 frame=NSRect:
{{0, 0}, {1280, 800}} title=nvim alpha=1.000000 isMain=0 isKey=0 isVisible=1 delegate=0x7f8122428600>>: 0.01134598255157471
Jun 23 16:07:34 xikinbook Docker[1293]: TCP 54.231.8.136:443 > 192.168.65.2:43050 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:34 xikinbook Docker[1293]: TCP 54.231.8.136:443 > 192.168.65.2:43052 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:36 xikinbook Docker[1293]: TCP 54.231.8.136:443 > 192.168.65.2:43056 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:37 xikinbook Docker[1293]: TCP 54.231.8.136:443 > 192.168.65.2:43060 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:39 xikinbook Docker[1293]: TCP 54.231.72.114:443 > 192.168.65.2:56746 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:39 xikinbook Docker[1293]: TCP 54.231.72.114:443 > 192.168.65.2:56744 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:40 xikinbook Docker[1293]: TCP 54.231.72.114:443 > 192.168.65.2:56752 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:42 xikinbook Docker[1293]: TCP 54.231.72.114:443 > 192.168.65.2:56764 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:45 xikinbook Docker[1293]: TCP 54.231.32.82:443 > 192.168.65.2:38440 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:46 xikinbook Docker[1293]: TCP 54.231.49.164:443 > 192.168.65.2:45828 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:46 xikinbook Docker[1293]: TCP 54.231.32.82:443 > 192.168.65.2:38458 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:47 xikinbook Docker[1293]: TCP 54.231.32.82:443 > 192.168.65.2:38460 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:47 xikinbook Docker[1293]: TCP 54.231.32.82:443 > 192.168.65.2:38462 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:48 xikinbook Docker[1293]: TCP 54.231.32.82:443 > 192.168.65.2:38472 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:48 xikinbook Docker[1293]: dropping unexpected TCP packet sent from 172.18.0.4:38472 to 54.231.32.82:443 (valid sources = 192.168.65.2, 0.0.0.0)
Jun 23 16:07:49 --- last message repeated 1 time ---
Jun 23 16:07:49 xikinbook Docker[1293]: TCP 54.231.32.82:443 > 192.168.65.2:38466 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:49 xikinbook Docker[1293]: TCP 54.231.32.82:443 > 192.168.65.2:38473 proxy failed with flow proxy b: Connection refused
Jun 23 16:07:52 xikinbook Docker[1293]: TCP 54.231.80.163:443 > 192.168.65.2:42694 proxy failed with flow proxy b: Connection refused

The diagnostic ID for the issue is: 4E31EDCC-F5EA-4162-AB49-929CB7EBFD94

And here is the output displayed in the Feedback & Diagnose window:

Docker for Mac: version: mac-v1.12.0-beta16.2
OS X: version 10.11.5 (build: 15F34)
logs: /tmp/20160623-163157.tar.gz
failure: docker ps failed: Failure("docker ps: timeout after 10.00s")
[ERROR]  docker-cli
         docker ps failed
[OK]     app
[OK]     menubar
[OK]     virtualization
[OK]     system
[OK]     osxfs
[OK]     db
[OK]     slirp
[OK]     moby-console
[OK]     logs
[OK]     vmnetd
[OK]     env
[OK]     moby
[OK]     driver.amd64-linux

Some information on my box:

% uname -a
Darwin xikinbook 15.5.0 Darwin Kernel Version 15.5.0: Tue Apr 19 18:36:36 PDT 2016; root:xnu-3248.50.21~8/RELEASE_X86_64 x86_64
Docker version: Version 1.12.0-rc2-beta16 (build: 9493)
f615be9fb245904fbdf1aa0cad251d418c869428