Given the scales we are talking about I think the lumberjack technique would not work. Lumberjacks walk away from a tree until they visually measure an angle of 45 degrees between the bottom and the top of the tree: at that point they are standing at a distance from the tree which is equal to its height, and which they can measure easily walking back to the tree. It only works because the lumberjack is small in comparison to the tree so model approximations such as "the eyes of the lumberjack are at ground level" or "the ground is perfectly horizontal" hold true enough to not impact the final result too much. I don't think it would work well enough on a rover and a 7" rock. Note that if you wanted to go this route anyway you could implement it with a camera or a laser rangefinder, and you could use any angle and trigonometry formulas.
Because the rock is small I would use a mechanical trick. Maybe use a pole with a sonar pointing down that you would place directly above the rock. You could use a pendulum to make sure it's vertical even if the rover is on uneven ground. Or you could develop a device like a forklift that you would place above the rock and progressively lower until you hit the rock. You would then know the height based on the position of the stepper/servo driving the lifting part.
That's the way I would go with this challenge, I encourage others to post their answers if they have different ideas because there might be plenty of other interesting solutions!