Yeah the dremel works for rough shaping the plastic stock that you'll use on the joint but it's too much for direct work on the model. Here's a couple of things that I've found out too over the years of messing things up. First, use your wife's emery boards for fine shaping. Sandpaper, even very fine grit, clogs pretty fast. A steel emery will let you tap it off as much as you need. Also remember you are working with plastics so don't use any sort of petroleum based chemicals to ease the removal of stuck parts. This includes vaseline, WD-40, stuff like that. A couple drops of Dawn does just as good and rinses cleanly after.
I've never used steel rods but I can see how it would work nicely on these. They are fairly beefy and tall so it might be called for. You really need to tease out the stuck balls and start with a clean model if it's at all possible. Once you see how the joints work then you can decide how to proceed.