What are some extra goodies to add in polish to make the animation stand out even more (eg. head squash and stretch…)
For me, the single biggest thing is pushing my arcs into something clear, fun, and pleasing to the eye. There's nothing like some beautiful arcs on the wrists, feet, nose, props, etc., to really bring a scene to life and take it from looking acceptable to looking great!
Other than that, especially in visual effects animation, which is the medium I've mostly worked in (animating characters who need to live in the same frame as live-action actors), the key is subtle complexity. It's finding small ways to add little secondary things that bring the character more fully to life.
Things like having a character swallow, and the intricate neck muscle movements that go into a swallow, for example. Or putting in breaths into the scene - expanding the chest a bit, etc.
As you say, you can also get some great extra mileage out of squashing and stretching the head slightly, if the style of the film is appropriate for that. In a more realistic film, you could get that feeling out of squashing/stretching the fleshier parts of the face while keeping the skull itself more rigid, but it's the same idea - giving the overall character a heightened feeling of being organic and fleshy.
All of these sorts of things - micro eye movements, muscles flexing/relaxing, ear twitches on an animal, toes squishing against the ground, etc - these all can add to the overall complexity that will help the character feel even more alive without sacrificing the subtlety of the performance!