I write scripts. I don't think there is a good method to measure asteroid thickness. The information you would get from cameras and/or sensors is a size description as a box. To get "thickness", that depends on where you are according to the asteroid and can quickly get weird. Picture an asteroid in the shape of a 'W' and you get different answers depending on direction, like you stated.

Hi ShadedMJ. Because you are familar with script, maybe you can answer to an idea. I tried with a sensor on top of a rotor and make the sensor range only in front direction (all other 0,1). Then you get a small beam in the direction of the current rotor position. In this way you can detect the start of the asteroid, but not the end. Is it possible to add to the sensor a minimum distance to the front direction?
If yes, you could set it to 5m start and 100m end, if the sensor does not detect the asteroid anymore, then the thickness is less then 5m. It will not be very precisly as you mentioned, but it would help me to stop drilling just in time.

Unfortunately, there is no minimum range for the sensor block. Also the default sensor maximum range is 50m so there are probably a lot of asteroids larger than 50m.