Ask yourself how much money your startup could eventually be sold for. $5 Million? $10 Million? Now divide that by the number of years, divided by 2000. For a $10M exit, working on the startup for 5 years, that works out to $1000 per hour. If you really think your startup can be sold for $10M or more within 5 years then you should think twice before taking on any contract work for less than $1000 per hour.
But even if we take your figures, assuming like the original question that you actually need the money, you're choosing between giving away time or giving away equity.
Assuming that delaying a couple of months doesn't diminish the value of your $10 million exit, then giving away even a only couple of percentage points in equity instead is giving away the difference between the ramen money and $200,000 in five years' time; that's the nominal gross return to the investor if you succeed.
Taking it further, if you take a ~$20,000 investment for ~5% of the company to save you ~200 billable hours of contract work at ~$100 per hour, in the event of a $10 million exit the opportunity cost of giving away equity instead of contracting (without any additional funding it's approx $500,000-$20,000 in this example) will have most likely been well in excess of $1000 per hour.
That's why people's chief motivation for joining incubators is seldom the seed money.