This, unfortunately, is an all too common issue. My perspective is from that of a compensation consultant that has worked with a lot of private companies and start-ups (among others)
First you must address WHY your base pay is so far below market.
Next you must address the concept of the phantom stock and what it's true potential can be over whatever term they have offered (is it just for the upcoming year...is it forever?)
Next you need to understand what potential ownership would even offer. Is there any possibility of an exit/lquidity event in the foreseeable future? If not, cash probably makes more sense, unless the company offers a well-funded cash out potential or buy-back plan.
"Low-balling" base pay is pretty common. Many company find it hard to make significant pay increases to get pay in line for key employees. If you clearly explain your situation they may reconsider and offer something more useful
You may want to consider getting some professional help. I would recommend talking to Mary Russell (mary@stockoptioncounsel.com). I work with the corporate side of these equations. Mary works with the individuals. She may be able to help put together an argument that convinces the right people.
Sadly, sometimes walking away is the best option. I would recommend that you first make sure your other possibilities are exhausted.