It looks like a standard type servo driving the gear train. Yes, you will gain torque but lose angular movement.
The servo will still only travel the standard movement, 120 degrees max? The output gear 30 degrees?

What's needed is the servo to be modified so it can travel round & round to drive the large output gear a reasonable
amount to gain angular movement. To control this you would need the feedback potentiometer on the shaft for the
large gear so the servo electronics know the position of the big, output gear.

You don't get anything for free, if you end up with 4 times the torque the output speed will be 4 times slower.