Render comment parts individually with Panels/Page manager?
There's no out of the box solution for doing this today.

If you look at a file like ctools/plugins/content_types/node_context/node_links.inc you'll see how it's done for nodes and their links. The other files in the same directory do the same but to different pieces of nodes. For historic reasons, there's a lot of Node specific content in there.

Today it should be possible to generalize the same approach onto all entities, but as far as I know, that hasn't happened anywhere.