Are these going to be "used"? Will they be sat on, pushed behind someone etc, or will they simply be sat on a chair for occasional use? If the latter, they aren't going to need to be washed often so you need not worry about the effect of washing on the interfacing. An alternative might be to mount the T shirt fabric onto a piece of woven cotton (sheeting for instance). To counteract the stretchiness of the T shirt, you could machine stitch in squares across, a bit like quilting maybe 4" apart. In a matching thread it wouldn't interfere with the design too much.