Why are my cookies falling apart?
I think there is a better explanation than the flour conversion. First, 4.25oz is on the low side as a conversion factor, Cookwise uses a factor of somewhere over 5oz. Second, we are talking about a recipe which started out as "flourless" and the author put in just enough flour to keep them from turning into puddles. I doubt that a bit more flour will ruin them, seeing that the initial amount was so low. 

Since you mention that you are from Europe, I think you have used the wrong sugar. The brown colored sugar sold in Europe is frequently just "raw sugar" or similar, which is the same as white sugar, but with somewhat darker color. It is completely dry, and melts a bit worse than white sugar. Both the falling apart and the "sugar taste" sound like you ended up crunching on this kind of crystals. 

When Americans bake with "brown sugar", they use gooey stuff where there are still lots of melasses clinging to the crystals. This stuff is wet, and sticks together. You can sometimes get it from specialty stores which import foreign products (UK shops will have it too). In many recipes, it is also an option to "make your own" by using a mix of white sugar and some syrup - melasses if you can get them, some other liquid "sugar" if you can't (beet syrup, agave syrup, golden syrup, etc.) This works well in other doughs where the sugar is added for taste. I am a bit more skeptical here, where it's not just the ratio of moisture that matters, but the wet sugar is a major structural component. Maybe you can mix it and leave it for a day or two before baking.