Rick Hartley has some pretty good presentations on this, with decent data and convenient rules of thumb. He makes a living by teaching this stuff, so I can't really share them.
A summary rule of thumb is this (ignoring a lot of convoluting factors): If your planes are more than 10mils apart, the interplane capacitance isn't effective in decoupling, so keep your capacitors as close as possible to the supply pins with the least inductive return path possible. With your planes at 1.2mm apart, this is probably on the opposite side of the board underneath a BGA. If your planes are less than 10 mils apart, make sure your capacitors are within the radius defined by the speed of signal propagation (based on the PCB's dielectric constant), and the fastest rise time of your part. The board capacitance is supplying all of the energy during the edge, and you want your capacitors to start replenishing that energy by the time the edge finishes.
Is there any reason you're not putting your power and return on opposite sides of a prepreg, rather than across the core? It sounds like you're working with a 1.2mm core, so with a standard 1.6mm board, your outer layer pairs are close enough to give effective board capacitance.