I think that the best improvement to your site would be to allow players to search by various criteria, so that the can find the exact
opponents that they want to play.
For instance, rather than search by name, search by:
1/. ranking range
3/. move frequency
4/. players with no restrictions
5/. recently moved players
6/. Opponent timeout periods
This would be a good idea as the player would not have to spending ages scrolling the public games and go into each individual players settings and would place more filters than is currently in place when just posting an open invite and hoping the right player responds.
It would be quicker and easier hand pick the perfect opponents and more of them.