How should I best connect the T3i to the H4N to record the H4N's audio both directly to the camera's input and record externally for safety?

They sell bundle kits if you haven't bought one yet over at B&H.

You need to run an attenuated cable because the line out of the Zoom is really hot. With that you can get a secondary backup recording inside the DSLR. They sell everything separately too.

Zoom H4N On-Camera DSLR Audio Kit H4N B&H Photo Video

I actually already have the Zoom.

Scroll down on the linked B&H page until you reach the "This Kit Contains" section. You need the Whirlwind attenuation cable. Order it separately.

Thank you.