Ok, I think I got it working by using "Island Group Stack Overlapped".
Island Groups / Stack Similar, or Island Groups / Stack Overlapped Have a similar effect. One stacks similar selected islands appart from one another. The other one stacks similar islands on top of one another. None of these two options enable the packing algorithm to take into account the stacked islands. Whether they're stacked similar, or stacked overlapped, they don't move anymore. Everything packs, they stay in place. That's a really big issue.
When stacked, islands are packed only if they are inside the main UDIM space. But packed stacked islands are computed differently as single islands (even when perfectly similar islands are stacked) and the packing results in a mess of overlapping islands.