I checked in file(location can differ on Ubuntu against Gentoo):
/usr/src/linux-4.8.6-gentoo/Documentation/sound/alsa/HD-Audio-Models.txt

for ALC3266 chip(which alsamixer is reporting) there is an entry:
ALC22x/23x/25x/269/27x/28x/29x (and vendor-specific ALC3xxx models)
======
  laptop-amic		Laptops with analog-mic input
  laptop-dmic		Laptops with digital-mic input
  alc269-dmic		Enable ALC269(VA) digital mic workaround
  alc271-dmic		Enable ALC271X digital mic workaround
  inv-dmic		Inverted internal mic workaround
  headset-mic		Indicates a combined headset (headphone+mic) jack
  headset-mode		More comprehensive headset support for ALC269 & co
  headset-mode-no-hp-mic Headset mode support without headphone mic
  lenovo-dock   	Enables docking station I/O for some Lenovos
  hp-gpio-led		GPIO LED support on HP laptops
  dell-headset-multi	Headset jack, which can also be used as mic-in
  dell-headset-dock	Headset jack (without mic-in), and also dock I/O
  alc283-dac-wcaps	Fixups for Chromebook with ALC283
  alc283-sense-combo	Combo jack sensing on ALC283
  tpt440-dock		Pin configs for Lenovo Thinkpad Dock support

So these are models we could refer in /etc/modprobe.d/alsa.conf(again can differ on Ubuntu)
I mixed it with probe_mask which is known to handle some issues:
options snd-hda-intel single_cmd=1
options snd-hda-intel probe_mask=1
options snd-hda-intel model=headset-mic

by using first model=generic I got working both speakers and headphones at same time. In the moment I am testing all scenarios and the result :-(

Here are available addresses of outputs:
[    6.763392] bus: 'hdaudio': really_probe: probing driver snd_hda_codec_realtek with device hdaudioC0D0
[    6.763393] snd_hda_codec_realtek hdaudioC0D0: no default pinctrl state
[    6.763972] snd_hda_codec_realtek hdaudioC0D0: autoconfig for ALC3266: line_outs=1 (0x17/0x0/0x0/0x0/0x0) type:speaker
[    6.763973] snd_hda_codec_realtek hdaudioC0D0:    speaker_outs=0 (0x0/0x0/0x0/0x0/0x0)
[    6.763973] snd_hda_codec_realtek hdaudioC0D0:    hp_outs=1 (0x21/0x0/0x0/0x0/0x0)
[    6.763974] snd_hda_codec_realtek hdaudioC0D0:    mono: mono_out=0x0
[    6.763974] snd_hda_codec_realtek hdaudioC0D0:    inputs:
[    6.763975] snd_hda_codec_realtek hdaudioC0D0:      Headset Mic=0x18
[    6.763976] snd_hda_codec_realtek hdaudioC0D0:      Headphone Mic=0x1a
[    6.763976] snd_hda_codec_realtek hdaudioC0D0:      Internal Mic=0x12
[    9.099842] driver: 'snd_hda_codec_realtek': driver_bound: bound to device 'hdaudioC0D0'
[    9.099850] bus: 'hdaudio': really_probe: bound device hdaudioC0D0 to driver snd_hda_codec_realtek
[    9.100055] bus: 'hdaudio': driver_probe_device: matched device hdaudioC0D2 with driver snd_hda_codec_generic
[    9.100055] bus: 'hdaudio': really_probe: probing driver snd_hda_codec_generic with device hdaudioC0D2
[    9.100057] snd_hda_codec_generic hdaudioC0D2: no default pinctrl state
[    9.100152] snd_hda_codec_generic hdaudioC0D2: autoconfig for Generic: line_outs=0 (0x0/0x0/0x0/0x0/0x0) type:line
[    9.101819] ALSA device list:
[    9.106806] snd_hda_codec_generic hdaudioC0D2:    speaker_outs=0 (0x0/0x0/0x0/0x0/0x0)
[    9.106806] snd_hda_codec_generic hdaudioC0D2:    hp_outs=0 (0x0/0x0/0x0/0x0/0x0)
[    9.106807] snd_hda_codec_generic hdaudioC0D2:    mono: mono_out=0x0
[    9.106807] snd_hda_codec_generic hdaudioC0D2:    dig-out=0x3/0x0
[    9.106808] snd_hda_codec_generic hdaudioC0D2:    inputs:
[    9.107716] driver: 'snd_hda_codec_generic': driver_bound: bound to device 'hdaudioC0D2'

And I also still see the nasty error:
[   32.543313] snd_hda_intel 0000:00:1f.3: azx_get_response timeout, switching to polling mode: last cmd=0x202a0000
[   33.546454] snd_hda_intel 0000:00:1f.3: No response from codec, disabling MSI: last cmd=0x202a0000
[   34.547426] snd_hda_intel 0000:00:1f.3: azx_get_response timeout, switching to single_cmd mode: last cmd=0x202a0000

which I thought with probe_mask=1 might be fixed.