As you already have pointed out, the problem is the mechanical interface between a step motor drive and the adjustable resistor. Besides the problems with force applied to the resistor, you also have to make sure that the mechanical interface hits the slot of the adjustment screw precisely. The slot may be in different positions.
Anyhow, if you need to make adjustments automatically maybe an "electronic adjustable resistor" would be an option. The drawback is that these devices are no longer adjustable manually, i.e. with a screwdriver.
There are several manufacturers, Maxim has quite a wide range of these devices:
http://www.maxim-ic.com/products/digi_pot/