Before you exercise, make sure you are familiar with the Alternative Minimal Tax and how exercising Stock Options affect it. See
https://www.wework.com/magazine/knowledge/startup-equity-und... and
https://gigaom.com/2011/06/05/5-mistakes-you-cant-afford-to-... (especially the David Weekly at the bottom). Some people went bankrupt for that. Also check the rules on ISO (I supposed you have ISO options).
Then I think the best you can do is to sell the right to own the stocks when you will be able to sell them according to your stock plan. In practice you cannot sell the stock now but you can have a contract with a person that you will sell them as soon as you can. Or something like that...
On how to find somebody willing to buy them, I am not sure. Common stocks are considered almost worthless by a lot of investors. There are also some information about preference in round of funding etc, that a sophisticated investor would like to know but it is not always public knowledge outside of the board.
Before Facebook IPO I know SecondMarket was the place. I am actually curious about the options here.