I would argue that there are more effective ways of dealing with saddle, knee and back discomfort than moving your feet around on your pedals. But then again, I'm not sure any of the fit issues I've had on my bikes would have been alleviated by moving my feet around more. Even if you don't go with clipless pedals, there are benefits to wearing a stiff-soled shoe.

Admittedly, you need to know how to set the cleats up correctly in the first place. Some people swear by float to address knees issues; some people insist that float hurts their knees. If you do go with a no-float cleat (like an SPD), then you really have to get it set up correctly or it will likely give you knee problems.

Have you talked to a fitter about your bike fit in general and/or clipless shoes?