If you don't need the accuracy then the last thing you should do is spend a fortune on components to get it!
I've got a CNC 4th axis on my home machine, which is simply a Vertex rotary table with a stepper motor on it. Works absolutely fine. The limiting factor with the backlash is that if you set the worm up for no slack at one point, somewhere else around the rotation the system will bind. There is a lot to be said for 'running in' the system. Just adjust as well as possible, and then set the table rotating continuously for half an hour or so. My system is really smooth after a few hours' use now. For a trunnion set up, you can't afford to have enough slack in the system that it will start vibrating in the backlash and cause finish problems. I think you should be able to get away with it though.