There are [three variables you can change on the camera](https://photo.stackexchange.com/questions/6598/what-is-the-exposure-triangle) to modify the exposure. Unfortunately in your case, you can't lower the shutter speed, you can't use a wider aperture and you're already unhappy with the grain so you don't want to raise the ISO any further. A new lens won't help you as you still need to keep the aperture narrow for your DoF requirements.

Therefore you have two options:

* Get more light onto the scene
* Get a sensor with better low-light performance. The T3i is certainly not class leading in this regard, so you could certainly do better. Note that moving to full frame isn't an obvious a win here as is it in other cases, as you'd again need to stop down to keep your DoF - but something like the Sony A7S, which is class-leading in its low-light performance would still help.