A probable answer is that maybe it wasn't intended to be firm at all.
There are different types of liverwurst in Germany. The most commonly sold one is indeed firm, but from its texture, I'd guess that it has gelatin added. It is more rubbery than the naturaly gelled meats I've eaten. But there is no guarantee that your recipe was intended for this kind.
Another common type is the spreadable liverwurst. It is a creamy mass which is intended to be spread on bread similar to cream cheese. If you want to make this kind, the meat grinder is probably only good for the first pass. I'd make sure to puree it really fine, a blender is probably better. (Unless you specifically want to make the chunky type).
I am not too sure that pork shoulder is such a good choice, probably the fat wasn't enough. The most popular recipes on chefkoch.de (a site similar in quality and popularity to allrecipes) call for pork belly, the part which is made into bacon. Some of them also say to add
speck, which is the non-rendered subcutaneous layer of fat of the pig. It also tends to come from the belly (sometimes from the back), but has less or no meat attached. Many specify that the meat gets cooked first, then ground. The raw liver gets ground separately (after removing fascia and the ducts). Then everything is mixed, pureed (or regrinded for chunky). Then it is filled (some use natural casing, most fill it into jars, nowhere was muslin mentioned) and sterilized. I found some variance among the methods, but as I haven't tried any of them, I can't tell you which works best. I didn't find a recipe which was explicitly for firm liverwurst, but many of them explicitly mentioned spreadable liverwurst.
I also found some discussion on the proper ratio. This varies (depending on taste) between the liver being 20% to 33% of the whole mass. A higher ratio seems to cause both dryness and bitter taste.
This is probably helpful if you can live with spreadable wurst. If you insist on the firm kind, you may have to experiment with gelatine, because I couldn't find any homemade recipes for that.
Edit: some more research suggests that the denaturing proteins in the liver are enough to bind the leberwurst to be firm, and adding some of the fatty water in which the meat cooked makes it spreadable. The one who wrote it seemed to have some authority on making sausages (at least he made lots of posts and the others didn't disagree with any of them). Again, this isn't my opinion, just a translated summary.