Four layer PCB power plane
The term that you're looking for (if you want to find more sources on this) is a split plane. It's used pretty often - you aren't doing anything out of the ordinary.

Just a few things to keep in mind:


You'll want a separate analog and digital ground on your ground plane.
Keep the planes aligned over each other - don't put your analog power planes over your digital ground. Check out page 4 of Splitting Planes - For Speed and Power.
Don't route traces that cross the boundaries of your power/ground powers. See PCB Stack-Up - Part 6. Return Path Discontinuities for some info on this.


You might be able to avoid the finger-shaped power planes if you're clever with component placement - in a pinch, you could try keeping the planes simple and using vias to connect the planes to some wide signal traces for the awkward power pins.