Stepper motor won’t turn once loaded
Holy cow. That's a real load for a little motor like yours. The problem is not weight, but moment of inertia. If you're going to do this stuff, you need to figure out how to calculate this. 

First, moment of inertia. For a disk of mass M and radius R, $$I_z = \frac{MR^2}{2} = \frac{(13.6 \text{ kg})({.43\text{m})^2}}{2} = 1.3$$ Since the nominal torque T of the stepper is .49 Nm, and 1/200th of a revolution is $$\Theta = \frac{2 \pi}{200} = .0314\text{ radians}$$ the nominal time for one step (starting from rest) is $$t= \sqrt{\frac{2\alpha}{\Theta}} = \sqrt{\frac{2T}{\Theta I_z}} = \sqrt{\frac{2\times .49}{.0314 \times 1.3}} = 4.9 \text{ seconds}$$ So your problem is that you're trying to step way too fast. Even manual stepping is, as you've discovered, unreliable. Your table is not terribly massive, although 30 lbs is more than you think, it's the large radius that giving you problems.

For this application, I'd recommend either a much beefier stepper, or a reduction mechanism to increase the torque at the table. Try putting a simple bearing at the axis, and use the stepper to drive the edge of the table (I'm assuming it's a circular table) using something like a 1" diameter rubber wheel - the smaller the better. This will give you a 30-fold increase in torque, with a starting step time of the order of 1 step/sec. You'll be able to ramp up the speed as the table rotates faster, so your total time will be less than 200 seconds for a revolution. But also keep in mind that you'll need a deceleration profile which matches the acceleration profile. The stepper will have exactly the same problems stopping the table that it had starting it.

EDIT - Oh yes, and your final load is not going to help. If it at all approximates a cylinder of the table diameter, since final mass is about 16 time the table mass, your step time will have to increase by a factor of 4.