serafis Great job! That's really helpful. So it turns out there is (are) issue(s) with HDMI and/or clock configuration for particular resolution. It makes sense that could be a problem. Audio packets are sent in blanking intervals between two consecutive frames. If this timing is off then there could be also audio issues. Can you please provide output of edid-decode /sys/class/drm/card0-HDMI-A-1/edid? This should tell what timings are communicated by your TV and AVR. I just tested 1360x768p @ 60 Hz on my TV and everything seems to work fine. I suspect that my TV is pretty forgiving for non-optimal configurations.
Regarding multi-channel configuration - I noticed that same format (iec958) is used also for non-passthrough (linear PCM) audio. This shouldn't be the case, so ALSA config needs some changes.