I don't know exactly what was used to secure linings to screws on bonded lining brake shoes, but It might be worth investigating. I'm not sure I'd trust screws instead of rivets, as screws can loosen, and don't have the cross section and shear strength that solid section rivets do for the same diameter. Even self-locking nuts can loosen.
I'm surprised that Jerry has recommended the less than original fix on brake systems given his statement above about the best repair being barely good enough.
