Since there doesn't seem to be a lot of movement on this problem ticket (PSCSX-2818), I started to search for other solutions. I found following addon: "Advanced Pack 5 - Create bundles of products". I've tested the demo shop and it looks like a good/better alternative for the standard Pack functionality in Prestashop. Pack products or bundles as they call it and individual products are separated by this addon, and it has a nice feature that can be used on the product page of your shop to indicate that a certain individual product is also available in a "bundle".
It's not a cheap addon so I wonder if anyone has experience with it and wants to share that experience. Or do you have other suggestions, addons, solutions?