So here is the solution, after 2 weeks of trying almost everything:
options snd_hda_intel position_fix=1
at the end of:
Reboot, and voila, problem gone.
What this does according to Alsa doc is: position_fix - Fix DMA pointer (0 = auto, 1 = none, 2 = POSBUF, 3 = FIFO size)
Why this is necessary only on my box and not other people's boxes I have no idea. Either I have something set differently in the bios regarding DMA, or perhaps bad memory or something, or my sound chip is a different release that's slightly different. If anyone would like to compare the revision of the chips by issuing some commands (maybe lspci with some options?) let me know...
Anyway, thanks to everyone who tried to help me, and hopefully this will help someone else in the future.