A timing belt drive would be the simplest way to go. And they are very reliable and accurate. I see the Automation Technologies unit is using a 6:1 timing belt reduction on one of their units, and what looks like a 20:1 gear drive on the other. I think either would work. You could just design & build your own system pretty easy, if you have access to some metalworking machines. A wood lathe would not be a bad place to start, it already has a headstock and a tailstock. Hanging a stepper motor on it is not too much of an engineering challenge, but will take some metal work that probably can be done on a router if you don't have metalworking equipment. There are a lot of chucks available that will mount on a wood lathe spindle.

If you wanted to direct couple you might have to build a coupler, but I would use a timing belt reduction. Better resolution and the torque is multiplied by the reduction. You don't need a lot of rotational speed, but you do need accurate indexing and holding torque.

As far as I know, there are no direct coupled 4th axis units in the hobby price range. Some of the high end industrial units have a huge, hollow shaft stepper or servo motor drive, where the motor is the rotating plate, but these are really expensive.