I finally found an answer to this problem based on this post from another forum (see "Attempt 1b" for reference). According to it, one can specify the module id, even if the driver used is the same:

alias char-major-116 snd
alias snd-card-0 snd-hda-intel
alias snd-card-1 snd-hda-intel

options snd cards_limit=2

options snd-hda-intel id=SB index=0
options snd-hda-intel id=HDMI index=1

thus yelding the correct card ordering and making sound work as expected:

$ aplay -l
**** List of PLAYBACK Hardware Devices ****
card 0: SB [HDA ATI SB], device 0: CONEXANT Analog [CONEXANT Analog]
  Subdevices: 1/1
  Subdevice #0: subdevice #0
card 1: HDMI [HD-Audio Generic], device 3: HDMI 0 [HDMI 0]
  Subdevices: 1/1
  Subdevice #0: subdevice #0

For applying to other similar cases, you can inspect /proc/asound for symlinks to your cards, they will be your desired modules IDs:

$ ls -l /proc/asound/
total 0
lrwxrwxrwx 1 root root 5 Jan 26 19:19 HDMI -> card1
lrwxrwxrwx 1 root root 5 Jan 26 19:19 SB -> card0
dr-xr-xr-x 4 root root 0 Jan 26 19:19 card0
dr-xr-xr-x 3 root root 0 Jan 26 19:19 card1
-r--r--r-- 1 root root 0 Jan 26 19:19 cards
-r--r--r-- 1 root root 0 Jan 26 19:19 devices
-r--r--r-- 1 root root 0 Jan 26 19:19 hwdep
-r--r--r-- 1 root root 0 Jan 26 19:19 modules
dr-xr-xr-x 2 root root 0 Jan 26 19:19 oss
-r--r--r-- 1 root root 0 Jan 26 19:19 pcm
dr-xr-xr-x 2 root root 0 Jan 26 19:19 seq
-r--r--r-- 1 root root 0 Jan 26 19:19 timers
-r--r--r-- 1 root root 0 Jan 26 19:19 version

I just managed to configure exactly this thanks to the instructions in the ArchLinux wiki :

Set the one sink - HDMI - in pavucontrol/Configuration, and the other - analog output - you specify in default.pa :

load-module module-alsa-sink device=hw:0,0
load-module module-combine-sink sink_name=combined
set-default-sink combined

Maybe you were missing the last two lines?

Addendum: This is OK to add the analog output to HDMI, but what if you want it the other way around? (I want to keep analog input, Pulse calls that "duplex"...) Unfortunately, load-module module-alsa-sink device=hw:0,3 did not work to add HDMI output to Pulse's "Analog Stereo Duplex" configuration. Pulse would start, but no HDMI output.

I compared the output of pacmd list-sinks in the two situations. When I added device=hw:0,3, that one would show up without ports. When HDMI output was chosen in pavucontrol, there would be ports. Looking at the output details, I came up with device=hdmi:0.

Choose "Analog Stereo Duplex" as your pavucontrol configuration, and add to default.pa :

load-module module-alsa-sink device=hdmi:0
load-module module-combine-sink sink_name=combined
set-default-sink combined

Works like a charm. I keep my microphone input, and on pavucontrol/Output Devices I have all options for analog output and for HDMI.