You're thinking of dark energy, the net effect of which is to change the overall expansion profile of the universe as a whole. Dark Matter was first proposed when galactic rotation profiles failed to meet theoretical expectations -- matter far from the center of each galaxy had a higher velocity than it would if visible matter had been the only factor.
> I think it's far more likely that our theory is incomplete rather than some whole new class of invisible matter/energy being conjured into existence
Occam's razor (the simplest explanation tends to be the right one) suggests that a new unobserved particle is more likely than abandonment of F = GMmr^-2 . This doesn't mean the equation must be correct, it's a question of reaching for the low-hanging fruit.
> So many non-scientists think dark matter is proven. It isn't. It's nothing but pure conjecture.
First, nothing is ever proven true in science, only false. Second, dark matter is more than pure conjecture, since there is observational evidence. A pure conjecture would be an idea about reality having no observational support at all (unicorns, Bigfoot). Dark matter is a hypothesis crafted to explain observations, but so far there's no persuasive theory to explain it, and no observations of candidate particles either.