What ingredient changes will make this cookie dough more workable?
Sounds an like you may just need more flour. That recipe has more fat per flour than common cookie recipes - for example, the canonical chocolate chip cookie recipe has 10 oz of flour for 1 cup of fat, while yours is only about 8 oz flour per cup of fat. So I'd definitely expect the dough to be on the soft side to begin with, and since the fat softens at it warms up, as you've seen, it just gets worse.

If your kitchen is on the warm side, it's possible that you'll also need to chill in the freezer instead of the fridge, but I'd certainly start with more flour (or less fat).