Out of curiosity, has anyone ever tried cheddaring an alpine make? E.g., follow the recipe for a basic Asiago or Montasio or some such up to the point where the curds are drained. Then cheddar the curds until pH = 5.3 or so, then mill and salt, then press. (As opposed to the typical alpine procedure of draining curds and pressing them until the cheese reaches pH 5.3 or so, and then brining or dry salting the cheese.) I've wondered what sort of difference this would make to the final results. Could something like this be what they mean by a "cheddar" that is a "hard Italian-type with notes of Swiss and Parmesan"??
If no one else here has tried this, then maybe for my next cheesemaking opportunity (which will not be until the end of the month, alas), I might give this a try, just to see what happens, and for the greater good ...