Questions,
I hope you can figure something out, I don't think there are exact answers. DD8 did ultimately find memorizing mult. and div. facts "fun" when she used Alek's because it became a game to her. In fact, the pressure of the speed element seemed to enliven her, but another child may have an opposite reaction.
I think it's a matter of preference. Lots of people will argue that mental calculation isn't of as much importance because of calculators. Our girls seem to posess their father's math aptitude, so they will learn the calculations and are great thinkers as well.
If a child is really resisting, it could be that they are not in a good place for certain learning at the moment. You could spend hours agonizing and pushing it, then both parent and child are miserable, when that child could easily and quickly learn it at a later time when they are ready.
We are all different in the way we learn and many of our paths will be different. Whatever works for you child is the best path for him IMO.
