try the before_content hook this will place it within the content container.
But what is the need for the Container Block around your Post Content ? For default layouts i would not wrap the content in a block as it just adds more padding.
I suggest that you remove the container block. You can shift click to select all of the inner blocks and from the toolbar menu select > Group – then you can simply drag the group out of the container and then ungroup them 🙂