There are two possibilities I can think of.
The first is there's a problem with mixing - you said you gradually add water, does that mean you start mixing it into the dough as you add it, or that you let it sit between additions? It looks like the recipe adds the water all at once, maybe lets it sit for a bit to hydrate, and then folds it all in together. If you're mixing in between each addition, your dough might not be wet enough, with parts that are getting overworked (which makes it stiff) and parts not getting hydrated as well (making it crumbly).
The other possibility is, you mentioned that the flour you're using is called white wheat flour. There is a kind of flour called "white whole wheat flour", which is functionally between the highly processed all purpose and regular whole wheat - if this is the case with your flour, you may not be adding enough water... whole wheat usually takes a little more water than all purpose flour, and I think it does better if given longer to hydrate.
In any case, even if your flour is different from white whole wheat, just being a different brand might be causing some of the problem, since all purpose is processed specifically to make it very predictable in recipes.
In either case, I would suggest sprinkling all the water the recipe calls for, plus a few teaspoons extra, and letting it sit a bit longer before you start to fold the dough. The extra water should make it a bit more pliable, and the dough being easier to fold should mean the fat has a better chance to stay in pockets with a looser dough flowing around it, so it doesn't get smooshed around into the flour as much because a stiffer dough means you need more force when mixing - which would make it crumbly instead of flaky.