I am also a software guy by profession. I've always liked tinkering with electronics, and have recently gotten into Arduino. It is an excellent platform for developing hybrid hardware/software solutions for problems like this. It is very easy to use, both hardware and software.
There is a large ecosystem of add-ons called "Shields" that just plug in. You can probably find a motor control shield that will do exactly what you want.
Your biggest challenge, I think, is going to be mechanical. How will you hold the polisher in position, and make a mechanism that will raise and lower it?
Off the top of my head what I come up with is a U shaped metal bar with a threaded rod in the opening of the U. You'd build a "sled" that would grip the bar and would have teeth that would grip the threaded rod. Then your would have a motor on the end of the assembly that would turn the threaded rod to move the sled up and down on the bar. You'd attach the polisher to the sled. You'd probably need a spring or rubber holder so that the polisher would press gently on the surface being polished but with some freedom of motion.