...and hoped that we could design a monetization system that didn’t exploit our players.
...we haven’t yet reached a level of revenue to even sustain operating expenses for the game
This all suggests you're generating some revenue but you don't mention how. Advertising? I'm genuinely curious.
I'm in a relatively similar predicament albeit an entirely different product. I run http://hackerjobs.co.uk with a good friend and it's been free to post for almost two years now. The site is generating more users & advertisers every week through word of mouth alone and at some point, if the site is to grow appropriately, we'll have no choice but to monetise it and I'm dreading it to be honest.