XPS 9350 DE - updated to Ubuntu 16.04 sound stopped working

I've recently updated to Ubuntu 16.04LTS and my sound and microphone stopped working. One of the reasons I wanted to upgrade was because I've read that support for external monitors using the D3100 dock is better in newer kernels (it's actually just as bad, DisplayLinkManager process still uses 30-50% CPU, monitor freezes from time to time etc.)

I've tried booting from a live usb with the same Ubuntu version and with that the sound does appear to work. However a clean install is NOT an option, I'm using this laptop for software development, and if I have to waste a few hours re-configuring my entire setup from scratch I will rather do it on a different laptop. The XPS 13 has been a huge disappointment.

Kernel version is 4.4.0-57-generic

$ aplay -l
**** List of PLAYBACK Hardware Devices ****
card 0: PCH [HDA Intel PCH], device 0: ALC3246 Analog [ALC3246 Analog]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: PCH [HDA Intel PCH], device 3: HDMI 0 [HDMI 0]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: PCH [HDA Intel PCH], device 7: HDMI 1 [HDMI 1]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: PCH [HDA Intel PCH], device 8: HDMI 2 [HDMI 2]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 1: Dock [Dell D3100 USB3.0 Dock], device 0: USB Audio [USB Audio]
Subdevices: 1/1
Subdevice #0: subdevice #0

$ sudo lspci 

00:00.0 Host bridge: Intel Corporation Sky Lake Host Bridge/DRAM Registers (rev 09)
00:02.0 VGA compatible controller: Intel Corporation Sky Lake Integrated Graphics (rev 0a)
00:04.0 Signal processing controller: Intel Corporation Skylake Processor Thermal Subsystem (rev 09)
00:14.0 USB controller: Intel Corporation Sunrise Point-LP USB 3.0 xHCI Controller (rev 21)
00:14.2 Signal processing controller: Intel Corporation Sunrise Point-LP Thermal subsystem (rev 21)
00:15.0 Signal processing controller: Intel Corporation Sunrise Point-LP Serial IO I2C Controller (rev 21)
00:15.1 Signal processing controller: Intel Corporation Sunrise Point-LP Serial IO I2C Controller (rev 21)
00:16.0 Communication controller: Intel Corporation Sunrise Point-LP CSME HECI (rev 21)
00:17.0 SATA controller: Intel Corporation Sunrise Point-LP SATA Controller [AHCI mode] (rev 21)
00:1c.0 PCI bridge: Intel Corporation Device 9d10 (rev f1)
00:1c.4 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port (rev f1)
00:1c.5 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port (rev f1)
00:1d.0 PCI bridge: Intel Corporation Device 9d18 (rev f1)
00:1f.0 ISA bridge: Intel Corporation Sunrise Point-LP LPC Controller (rev 21)
00:1f.2 Memory controller: Intel Corporation Sunrise Point-LP PMC (rev 21)
00:1f.3 Audio device: Intel Corporation Sunrise Point-LP HD Audio (rev 21)
00:1f.4 SMBus: Intel Corporation Sunrise Point-LP SMBus (rev 21)
3a:00.0 Network controller: Intel Corporation Wireless 8260 (rev 3a)
3b:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS525A PCI Express Card Reader (rev 01)
3c:00.0 Non-Volatile memory controller: Toshiba America Info Systems Device 010f (rev 01)[/code]