Not everyone is motivated by the same things, and you may be encouraging behavior you don't actually want. Let's examine your current assumptions that I'm guessing you hold if you think posting charts with names is effective:
* Everyone wants to be the best among their peers
* Everyone wants to be known as the best
* Everyone feels they can be the best
* Doing the most of some activity means you are the best at it
Here's the truth though:
* Not everyone is interested in competing
* Not everyone enjoys public recognition
* If there's a best, there must be a worst, and it's probably going to be the same people in the top 50% and bottom 50% on a regular basis
* Making more posts or slapping a grade on the most papers does not mean you are actually doing your job better
People who don't like competition will ignore your graphs. People who dislike being publicly recognised as being better than their peers will actively try to score lower. People who feel they can't compete even if they wanted to will come up with an excuse to ignore your graphs. Those who do like all those things will behave in a way that strictly improves their metrics, even if it is detrimental to the students (think many short posts with a minimum of effort rather than long, thoughtful, helpful posts).
There's almost no way posting your metrics will improve performance. You need to very carefully consider which behaviors you want to reinforce, how you will reinforce that behavior for each person. Being publicly declared the most helpful TA will thrill someone or mortify them. There is no single tactic that will motivate every person. You'll need a combination of talking to your TAs and trial and error to figure out what works.
I would strongly recommend avoiding tracking how many of X each person does. Your issue isn't that some people are grading more assignments than others in the same amount of time; the problem is some people are taking long breaks. And why wouldn't they? Grading isn't fun, and a break has an immediate and guaranteed reward of not having to grade during the break. Instead, change your process so one person taking breaks doesn't cause another person to do more work, or limit the breaks to specific times when the whole group breaks together.
In short, focus on the behaviors that you want to increase/decrease, then figure out what each person considers a reward. Then give out those rewards when you get the behavior you want.
There are whole books on this topic if you really want to get into it.