I realize you posted this months ago, but I was wondering if you went back to using individual jars and, if so, were you pleased with the results.
I use old straight knitting needles and sometimes metal skewers (clean, of course). I have some plastic smallish boxes that have openings on the sides and they work pretty well, but I do have the problem you had. Sometimes I move the box a little and that helps. Mostly, I just slip out of my shoe and try to fix it with my foot, which works just often enough that I try that before hitching the yarns on a peg and bending over and fixing the problem.