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, you may want it that way. Alternatively, reduce the sugar a little. To increase the influence of the onions, slice instead of chopping. Increase the butter, to make up for the decrease in fat in the cheese.
Medieval recipes can be reasonably explicit, when they want to.
These 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. Don't worry about it. The first three of these variations, while giving a wide range of effects, can all be described as straightforward interpretations of the originals.