There are three variables you can change on the camerathree variables you can change on the camera 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.