Hi!
In my case pcb is high speed (single impedanse 50ohm, differential 100ohm), and routed signals on L1,L,L6 layers must have GND plane for robust signal integrity. In my opinion in your case pcb is high speed too. In my board there are 4 different powers and i route them on one layer (L4).
I think you should try route VCCs on one plane, and have GND planes under(or above) each signal layer for robust signa integrity (especially if there are ddr or modern high speed interfaces)