Very sexy, indeed. But there is a catch (isn't there always?) - the press shown in the picture has a fixed and extremely high mechanical advantage (MA). As best I can tell, measuring from the picture, the upper lever has an MA of around 11. The lower lever has an MA of around 4. And the pulley will add an MA of 2. Multiplied together, and you get an MA of 88x - and again, this would be fixed, not adjustable. This has some very important implications:
On the positive side, it would be simple to put a great deal of force of weight on the cheese - 5 lbs applied to the end of the chain would produce 440 lbs of force.
On the negative side, it would be much more fiddly to put small amounts of weights on the cheese To follow a regimen of, say, 5, 10, 20, 40 lbs of pressing for an alpine style, you will need weights of .059, .11, .23, and .45 lbs. No, not too hard for a machinist to make, but not something you can easily do with a jug of water. To put this in perspective, with an 88x mechanical advantage, a change in just about 5 grams applied - a teaspoon of water - would produce a change in force of 1 lb. (Yes, I know - mixing my measurements - but for the metric folks, the relationship is easier to understand, and most of us who use pounds and pints still have some sense of what 5 grams "feels" like.) You may be thinking, "no problem - just hang a jug and put in a teaspoon of water for every pound desired." Yes, but first you need to weight the jug, very precisely, and factor that in, and you need to make sure you are using exactly a teaspoon of water each time, and above all, even after you've done all of this, you need to take into account the friction in the mechanism, which will throw all of your calculations out the window. IOW, you'll need to do some very careful calibration ...
But here's the real negative: with a fixed 88x MA, your weight on the pulley will have to move 88" in order for the cheese to compress by 1" - even when you are only pressing lightly. Since the first pressing of a cheese can easily compress by 2-3", that means a LOT of adjusting with the screw mechanism, every few minutes, to keep the weight from hitting the floor. Even once the cheese begins to compact, a movement of only .10" on the ram will require nearly 9" of movement on the weight - so even at the end of the process, you may be having to watch out that your mechanism has not "bottomed out."
All of the above is why I wanted a design that had adjustable MA, so that I could use high MA only when I really need a lot of force, and lower MA when I need more control.