You will have a hard time getting a taxi, Uber OR Lyft on NYE. Almost impossible, really. The lines will be long for taxis, and if you can even get an Uber, it will be surge pricing. Plus, Disney shuts down MANY roads in and out to facilitate contraflow for traffic leaving the parks.
The taxi line this year at Epcot was essentially three hours long, and even though you might be waiting in line for a cab, people were so frantic they would jump in front of cabs or even try to take your cab from you. Total chaos. Thanks, Mears!
I was once able to get an Uber at 3 a.m. at the Poly. But then it still took an hour to get to AOA, and it cost me over $50.
Your best bets are staying at a resort next to the park you plan to spend time at, joining the masses waiting in line for the resort buses after the fireworks - or renting a car and driving yourself.
I've done the past four years of NYE at Epcot, two times staying offsite, two times staying on. I will never go to a park unless I either drive myself or can walk back to my room. It's a disaster unless you want to spend at least an hour waiting in line for a bus.