The tax if exercising at this point two years down the road might have hurt.
What you describe -- and as someone that was bit by the AMT wrt ISOs, I recommend -- is exercising as soon as they vest to minimize the gain between the strike price and the fair market value at time of exercise. If the FMV goes up, you're going to be stuck paying the AMT on the spread, and not even be able to sell your shares to cover the tax, because pre-IPO stock is effective illiquid. If you wait until after the post-IPO lockout date to exercise, you'll pay even more in taxes, but at least you can sell some stock to cover it. Ironically, this is actually less painful, because you actually have liquidity.
If the company needs the cash more then maybe they'll let you keep the unvested shares, but since your usually-Common-Stock strike price is typically a lot less than what investors will pay for their Series-X shares it's likely they'd rather take back the Common Stock (?) even in cases of one or more transpired or likely down rounds (?).