According to the
Mears Taxi Fare Estimator (all taxis that pick up at WDW are owned by Mears), the estimated taxi fare from Disney's Polynesian to Orlando Int'l is now $64.00*. ("* Please note that the fare listed below is only an estimate and will vary depending on route taken, time of day and traffic conditions," according to the estimator.)
Add a tip and possibly a small delay along the route, and the taxi is likely to cost around $75 to $80. You can also reserve a towncar service. The cost will be similar.
In either case, as others have noted, you'll only get an extra 30 minutes or so of sleep, compared to using DME.
Another idea is to spend the final vacation night at the Orlando Airport Hyatt. You would check out of the Polynesian one day earlier, leave your bags with bell services, take DME to the airport in the evening (with your bags), and check in at the Hyatt. When you wake on the morning of your flight, you would already be in the airport terminal.
The Hyatt is not cheap, but it should cost quite a bit less than Disney's Polynesian. And it eliminates the need to consider a $75-80 taxi.