My solution to the conundrum of spiral galaxy rotation is that gravity increases towards the rotational plane of the spiral galaxy. The further the stars are from the central bulge, the closer they are to the plane of angular momentum of the galaxy. This seems to fit well with the general description of a spiral galaxy seen edge-on. Why hasn't anyone thought of this simple idea before? It even overcomes the problems associated with the second paragraph of the quote below:
Tinkering with gravity
There are two obvious explanations for the large discrepancy between the directly observable luminous masses of galaxies and clusters and the masses implied by their rotation and internal motions: either these systems contain very large amounts of unseen dark matter, or the Newtonian law of gravity breaks down on the scales of these objects. Whereas the former idea is the widely favoured paradigm of our time, as early as the 1960s some theoreticians began to suggest that instead of invoking a load of dark matter to provide the required extra gravitational influence, perhaps the flat rotation curves of galaxies could be explained by changing the law of gravity. One of the first suggestions was that at large distances, or beyond a certain particular distance, the strength of gravity might decrease more slowly than the Newtonian inverse square law implies, in which case the orbital speeds of distant bodies (such as stars and gas clouds in the outer regions of galaxies) would no longer decline in the same sort of way as the orbital speeds of the planets decrease with increasing distance from the sun.
One major problem about relating any change in the law of gravity purely to distance is that the bigger the galaxy, the more its rotational motion would deviate from Newtonian law, and the larger its apparent mass discrepancy would become. This does not match well with the observations - there are plenty of examples of small galaxies with large amounts of 'missing mass' and, on the other hand, examples of large galaxies, where the shortfall in mass is small. (The Dark Side Of The Universe, Iain Nicholson 2007)