I need to combine/merge existing movie symbol layers into one layer to animate them as one solid group. The equivalent would be creating a nested composition in After Effects, but I can't seem to find how to do this. How can I accomplish this?
Anything you want to animate as a single unit must be copied into a single symbol (graphic or movieclip). So get copying and pasting!
I can paste the existing symbols all as one solid object, but the animation/keyframes don't copy over...
That's what right-click Copy Frames is for. Handles multiple (contiguous) layers as well. Or just duplicate the entire movieclip and delete what you don't want.
If I understand your question correctly, Timeline Block To Symbol is your best option: