If aging for more than 3 months, than you want to cook it a little more.
From the same document:
"Nach bereits zwei Wochen ist das Mutschli genussreif, allerdings noch sehr mild im Geschmack. Nach drei Monaten ist ein Mutschli dann endgültig ausgereift, von diesem Moment an wird es nur noch schärfer im Geschmack und irgendwann ungeniessbar."
After just 2 weeks the Mutschli is suitably ripe, though very mild in flavor. After 3 months is a Mutschli then completely ripened, from this moment on it only becomes sharper in flavor and sometimes inedible.
That is to say, 3 months is about as far as you want to go.
The sharpness described here is not the same thing we mean when we in America talk about sharpness of a cheese (in German, the word reif, meaning ripe, is generally used) This is a bad quality. Remember that the Swiss like their cheeses in general far far stronger (Reifer, or sharper in American terminology) than Americans typically are accustomed to. If you don't believe me, eat an 18 month Emmentaler some time.
So if you want a 4 month cheese, you have to dry the mass out a little bit more, maybe cook up to the 110 to 115 F range.
Note one thing, with hard cooked cheeses, undesirable bacteria are most generally killed off. But the temperature ranges of this cheese are far too low for that. You will want to be sure and be very sanitary and have a good culture. And yes, the culture is thermo.
More specifically, you will want to use an Alpine type culture with Streptococcus Thermophilus and some form of Lactobacillus. (likey going to be either l. delbrueckii or l. helveticus)
Regarding the dynamics of the alpine cheeses there is one more thing that should be said.
The lower cooked cheeses ripen much faster than the harder cheeses, but the harder cheeses ripen better. The biggest reason for this is that the softer cheeses have a much more diversified bacteria population, whereas the harder cheeses have had their bacteria reduced by cooking to a small number of cultures.
Also, the higher moisture content is a little more hospitable to bacteria growth so they multiply slightly faster. Also, a moister cheese is more inviting to secondary population by bacteria post-make.
Part of the reason why a Mutschli becomes inedible once it is too old is because undesirable bacteria will produce much more pronounced false flavors past this point. This is much less of a concern if you start of with pasteurized milk. However, the principle still stands that a 4 month Mutschli is past its prime.
I should also note that the difference between the production an Emmentaler and an Alpkäse is 3 degrees (F) that is, Emmentaler may be cooked to about 122, while Alpkäse would be cooked to 124 or 125. This slight difference has a tremendous effect on the texture and hardness of the cheese (also, yes ps has an effect on texture as well) This is only here to point out how important it is to be precise with temperature and time on these cheeses. Slight errors can make a huge difference.