Because these are softer and more liquid, you may want to slightly reduce the eggs, say to five instead of six. This will also make the tart sweeter, but with these cheeses, that may be appropriate. Alternatively, reduce the sugar. Going further afield yet, many people today like swiss, or cheddar, or a mixture of them. Substitute them, increasing the butter, to make up for the decrease in fat in the cheese.
Medieval recipes can be explicit, when they want to.
These two aren't, presumably because they don't much care. Furthermore, when you make cheese, what precise cheese you get depends on everything from the precise set of wild yeasts in your buttery to the relative humidity. With a few exceptions, uniformity in cheeses is a modern artifact. The first three of these variations, while giving a wide range of effects, can all be described as straightforward interpretations of the originals. The fifth is more of a departure, but again, in a reasonable and justifiable direction.