Perhaps we could try to come up with some new ideas for membership benefits that makes it more attractive.
Common ideas for premium stuff I have seen elsewhere are cosmetics, like having gifs as avatars or special emojis (which we currently don't have at all). Then maybe some way to customize the site for yourself, for example choosing between different board schemes for some games could fit into this (Hex has a couple). For game of empathy perhaps you could be able to submit expressions to be used. I'm sure there is a couple things that could be done, but that's all I can come up with right now.
I would love to have the possibility of sorting my games. Sometimes I have 50+ moves to play (usually 20-30 moves to play) and skipping through all games in which I am not ready to move yet is really troublesome. If I would be able to sort games into two categories (games, in which I will be probably ready to answer my opponent after his next move, and games, in which I need a lot of time to think about move), that would be a big help. Such tool is very useful, but not "pay to win", so should be a nice premium option.