Free advice. Worth every cent. Double your money back, if not satisfied.
This is an industrial project. Coal and the associated dust. Expense less than a couple hundred bucks. Trivial, if it is bulletproof.
Optical sensors with a coating of coal dust won't be accurate, if they work at all. I don't know about ultrasonic.
Microswitches can be dust-proofed like this one, or something similar.
http://www.ebay.com/itm/5-LOT-TEMCo-HEAVY-DUTY-15A-Micro-Limit-Switch-Roller-Lever-Arm-SPDT-Snap-Action-/281125093036?pt=LH_DefaultDomain_0&hash=item41745c7eac
If you can find one that is described as "dust proof" so much the better.
Put the microswitch at the top of the test plate.
Put the test sample ring on the test plate such that it presses against the microswitch, closing the contacts.
A servo motor, no matter how powerful is not going to lift a steel plate and 5 or 10 pounds of payload. You can't use them in forklifts, either. They are also not dead-nuts accurate.
Use a Nema 23 or better stepper motor and a 10 tpi 1/2 threaded rod to lift the top edge of the plate until the microswitch trips and and immediately stop the stepper.
Use the number of steps at stop time to determine the angle. Return the stepper to home and display the degrees on an LCD screen. Use a pushbutton to reset the machine. Use two pushbuttons pressed simultaneously to start the machine. They should be far enough apart so that the operator cannot start the machine with one hand. There must also be an emergency stop button (a big, red one).
The number of steps per number of degrees can be found by experimentation.
Write a sketch that will step up/down by button press until you have found 1 degree with a magnetic inclinometer . If you have a repair department at your company, they will probably have one. They are relatively cheap.
Make a note of the number of steps for 1 degree.
Do the same thing for all the rest of the angles of interest. Depending on level of accuracy needed, you may want to do this for the 0.5 degree steps. Organize the collected information into a couple of arrays with degrees in one and the number of steps in each corresponding degree.
Use the steps per degree array in your sketch to convert steps to degrees. Since the edge of the table enscribes an arc, the number of steps per degree will vary, so don't try to skimp on this process. If you or some willing mathematician want, this could be calculated, but I don't have the skills to tell you how.
You could calculate fractional degrees from the steps per degree for the range in question, but don't try to come up with an average steps per degree and use it for all. This is industrial equipment. Accuracy counts. The Arduino has more than enough memory to satisfy your needs.
You will need to completely safety shroud the device. Pinched off fingers are frowned on in the corporate world. Pretty much everywhere else, I suspect.
Remember, anything worth doing is worth overdoing.
Looks like an interesting project.
Luck, John