I tested with the new 367.44 drivers, to be thorough, but they result in the same lockup scenario.
I installed these drivers using the official Nvidia .run package, just to rule out any issues with the build process or Ubuntu graphics-drivers PPA.
Aug 24 13:22:53 sager kernel: [ 18.954515] nvidia: module license 'NVIDIA' taints kernel.
Aug 24 13:22:53 sager kernel: [ 18.957924] nvidia: module verification failed: signature and/or required key missing - tainting kernel
Aug 24 13:22:53 sager kernel: [ 18.963393] nvidia-nvlink: Nvlink Core is being initialized, major device number 246
Aug 24 13:22:53 sager kernel: [ 18.963406] NVRM: loading NVIDIA UNIX x86_64 Kernel Module 367.44 Wed Aug 17 22:24:07 PDT 2016
Aug 24 13:22:53 sager kernel: [ 18.972016] nvidia-modeset: Loading NVIDIA Kernel Mode Setting Driver for UNIX platforms 367.44 Wed Aug 17 21:54:40 PDT 2016
Aug 24 13:22:53 sager kernel: [ 18.973164] [drm] [nvidia-drm] [GPU ID 0x00000100] Loading driver
Aug 24 13:22:53 sager kernel: [ 19.423917] input: HDA NVidia HDMI/DP,pcm=3 as /devices/pci0000:00/0000:00:01.0/0000:01:00.1/sound/card1/input19
Aug 24 13:22:53 sager kernel: [ 19.423977] input: HDA NVidia HDMI/DP,pcm=7 as /devices/pci0000:00/0000:00:01.0/0000:01:00.1/sound/card1/input20
Aug 24 13:22:53 sager kernel: [ 19.424040] input: HDA NVidia HDMI/DP,pcm=8 as /devices/pci0000:00/0000:00:01.0/0000:01:00.1/sound/card1/input21
Aug 24 13:22:53 sager kernel: [ 19.424088] input: HDA NVidia HDMI/DP,pcm=9 as /devices/pci0000:00/0000:00:01.0/0000:01:00.1/sound/card1/input22
Aug 24 13:22:54 sager kernel: [ 34.110289] nvidia-modeset: Allocated GPU:0 (GPU-e2f980da-ea7e-4335-6ae3-41ae731aed6d) @ PCI:0000:01:00.0
Aug 24 13:22:54 sager kernel: [ 34.158758] NVRM: GPU at PCI:0000:01:00: GPU-e2f980da-ea7e-4335-6ae3-41ae731aed6d
Aug 24 13:22:54 sager kernel: [ 34.158761] NVRM: Xid (PCI:0000:01:00): 61, 1362(3368) 00000000 00000000
Aug 24 13:23:01 sager kernel: [ 41.182295] nvidia-modeset: WARNING: GPU:0: Lost display notification; continuing.
Aug 24 13:23:04 sager kernel: [ 43.933741] nvidia-modeset: ERROR: GPU:0: Idling display engine timed out: 0x0000957d:0:0:0x00000040
...
Aug 24 13:23:28 sager kernel: [ 68.112255] NMI watchdog: BUG: soft lockup - CPU#3 stuck for 22s! [Xorg:5117]
Aug 24 13:23:28 sager kernel: [ 68.112258] Modules linked in: pci_stub vboxpci(OE) vboxnetadp(OE) vboxnetflt(OE) cmac bnep vboxdrv(OE) binfmt_misc nls_iso8859_1 snd_hda_codec_hdmi arc4 snd_usb_audio snd_usbmidi_lib btusb btrtl snd_hda_codec_realtek snd_hda_codec_generic nvidia_drm(POE) nvidia_modeset(POE) nvidia(POE) i915_bpo iwlmvm mac80211 intel_ips i2c_algo_bit intel_rapl snd_hda_intel x86_pkg_temp_thermal snd_hda_codec intel_powerclamp kvm_intel snd_hda_core kvm snd_hwdep irqbypass snd_pcm iwlwifi joydev snd_seq_midi snd_seq_midi_event cfg80211 snd_rawmidi input_leds serio_raw snd_seq rtsx_pci_ms snd_seq_device memstick snd_timer drm_kms_helper snd drm soundcore fb_sys_fops syscopyarea mei_me sysfillrect sysimgblt mei hci_uart btbcm btqca btintel bluetooth shpchp intel_lpss_acpi intel_lpss mac_hid acpi_pad coretemp parport_pc ppdev lp parport autofs4 btrfs xor raid6_pq drbg ansi_cprng algif_skcipher af_alg dm_crypt hid_generic usbhid mmc_block rtsx_pci_sdmmc mxm_wmi crct10dif_pclmul crc32_pclmul aesni_intel aes_x86_64 lrw gf128mul glue_helper ablk_helper cryptd psmouse r8169 ahci rtsx_pci mii libahci wmi i2c_hid pinctrl_sunrisepoint hid pinctrl_intel video fjes
Aug 24 13:23:28 sager kernel: [ 68.112355] CPU: 3 PID: 5117 Comm: Xorg Tainted: P OE 4.4.0-9134-generic #53-Ubuntu
Aug 24 13:23:28 sager kernel: [ 68.112356] Hardware name: Notebook P65_P67RGRERA/P65_P67RGRERA, BIOS 1.05.13RLS1 02/02/2016
Aug 24 13:23:28 sager kernel: [ 68.112357] task: ffff88084a682c40 ti: ffff88084bfc0000 task.ti: ffff88084bfc0000
Aug 24 13:23:28 sager kernel: [ 68.112358] RIP: 0010:[<ffffffffc15b39c0>] [<ffffffffc15b39c0>] _nv001865kms+0xd0/0x120 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112367] RSP: 0018:ffff88084bfc3718 EFLAGS: 00000283
Aug 24 13:23:28 sager kernel: [ 68.112368] RAX: 00000000000000dc RBX: ffff880828156008 RCX: 0000000000000000
Aug 24 13:23:28 sager kernel: [ 68.112368] RDX: 0000000000000000 RSI: 000000000062c411 RDI: ffffffff81e27b80
Aug 24 13:23:28 sager kernel: [ 68.112369] RBP: ffff880087549000 R08: 0000000000000001 R09: 0000000000000004
Aug 24 13:23:28 sager kernel: [ 68.112370] R10: 0000000000000020 R11: 0000000000000000 R12: 00053ad55f6f1a7d
Aug 24 13:23:28 sager kernel: [ 68.112370] R13: 0000000000000001 R14: ffff880849d4af08 R15: 0000000000000001
Aug 24 13:23:28 sager kernel: [ 68.112371] FS: 00007fecd71efa40(0000) GS:ffff8808764c0000(0000) knlGS:0000000000000000
Aug 24 13:23:28 sager kernel: [ 68.112372] CS: 0010 DS: 0000 ES: 0000 CR0: 0000000080050033
Aug 24 13:23:28 sager kernel: [ 68.112373] CR2: 000055be9b737474 CR3: 000000082143e000 CR4: 00000000003406e0
Aug 24 13:23:28 sager kernel: [ 68.112374] DR0: 0000000000000000 DR1: 0000000000000000 DR2: 0000000000000000
Aug 24 13:23:28 sager kernel: [ 68.112374] DR3: 0000000000000000 DR6: 00000000fffe0ff0 DR7: 0000000000000400
Aug 24 13:23:28 sager kernel: [ 68.112375] Stack:
Aug 24 13:23:28 sager kernel: [ 68.112375] ffff880828156008 0000000000000000 ffff880828155808 00000000c15a6d35
Aug 24 13:23:28 sager kernel: [ 68.112377] 0000000000000000 0000000000000001 ffff880828155808 ffff880828156008
Aug 24 13:23:28 sager kernel: [ 68.112378] ffff880828155808 0000000000000001 00000000ffffffff ffffffffc15aad93
Aug 24 13:23:28 sager kernel: [ 68.112379] Call Trace:
Aug 24 13:23:28 sager kernel: [ 68.112385] [<ffffffffc15aad93>] ? _nv001762kms+0xa3/0x110 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112394] [<ffffffffc15c5e08>] ? _nv001994kms+0x1ca8/0x2300 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112399] [<ffffffffc15923e0>] ? nvkms_alloc+0x50/0x60 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112403] [<ffffffffc1593530>] ? _nv000325kms+0x30/0x30 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112407] [<ffffffffc159355e>] ? _nv000334kms+0x2e/0x40 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112411] [<ffffffffc15940f1>] ? nvKmsIoctl+0x161/0x1e0 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112415] [<ffffffffc1592d95>] ? nvkms_ioctl_common+0x45/0x80 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112420] [<ffffffffc1592e41>] ? nvkms_ioctl+0x71/0xa0 [nvidia_modeset]
Aug 24 13:23:28 sager kernel: [ 68.112468] [<ffffffffc09cf080>] ? nvidia_frontend_compat_ioctl+0x40/0x50 [nvidia]
Aug 24 13:23:28 sager kernel: [ 68.112506] [<ffffffffc09cf09e>] ? nvidia_frontend_unlocked_ioctl+0xe/0x10 [nvidia]
Aug 24 13:23:28 sager kernel: [ 68.112508] [<ffffffff81220c3f>] ? do_vfs_ioctl+0x29f/0x490
Aug 24 13:23:28 sager kernel: [ 68.112510] [<ffffffff8120f811>] ? __sb_end_write+0x21/0x30
Aug 24 13:23:28 sager kernel: [ 68.112512] [<ffffffff8120d41d>] ? vfs_write+0x15d/0x1a0
Aug 24 13:23:28 sager kernel: [ 68.112513] [<ffffffff81220ea9>] ? SyS_ioctl+0x79/0x90
Aug 24 13:23:28 sager kernel: [ 68.112515] [<ffffffff8182df32>] ? entry_SYSCALL_64_fastpath+0x16/0x71
Aug 24 13:23:28 sager kernel: [ 68.112516] Code: 44 21 f8 41 39 c5 74 45 e8 ce eb fd ff 44 8b 9b 88 04 00 00 45 85 db 75 e4 49 39 c4 73 df 48 8b 4c 24 08 49 8b 44 ce 60 8b 40 04 <41> 39 86 b4 00 00 00 75 c9 48 8b 7c 24 10 48 c7 c2 f8 a8 60 c1
At the point where LightDM should start, the display briefly flashes from a screen with an underline cursor on the top left to a flat black/zero-brightness black screen and then back to the underline cursor. After that, the system is hung hard until I do a REISUB reboot.
Removing 367.44 and reinstalling 364.19 always works fine. Anything newer than 364 causes these hangs.