What is the best way to motivate teaching assistants?
I think the best way to motivate a person in academia is to give them a bit of job security, some funding which enables them to follow their interests, and a great team to work with. I am not sure if you can realistically give "your(sic!) TAs" any of this. 

In absence of solid motivating factors, you are trying to engage the team in some form of internal competition, which may motivate some people and completely put off others. For example, I personally would be puzzled as to why should I compete for some statistics or evaluations which look rather meaningless unless it has any effect on my promotion or chances of future employment. 

Most people I worked with responded well to:


smart goals
positive example
cutting the crap (including crap meetings)


In my experience, teaching is rather a pleasant activity and there is a lot of gratification in the  process of working with students. An excessive amount of paperwork, bureaucracy and management can only spoil the fun.