Adding copper between signals to reduce crosstalk only works if the copper is effectively grounded at the frequency of interest. For audio, it can potentially help. But for high speed clocks, it will likely make the crosstalk worse since the fill copper has high impedance to GND (relatively speaking).
To reduce crosstalk, focus on leaving lots of space around the potential aggressor signals such as clocks. The worst thing you can do is route them along side each other or directly over/under without a ground plane between.
Think of it this way. Two traces next to each other act as terminals of a capacitor. The gap between them is the dielectric. A wider gap means less capacitance, and therefore less crosstalk. Adding copper to the gap has the same effect as using a thinner gap (more crosstalk), unless that copper is grounded well. And at high frequencies, it is just not possible to ground that copper well.
So there may be good reasons to flood the outer layers with GND copper. It is often done. But adding copper between aggressor and victim signals will probably not reduce crosstalk. Use a large gap instead.