It is 65 miles from Heathrow to Stansted. Good roads - freeway most of the way - and on a Sunday morning you could do it in 75mins.
To clear LHR and get in STN will take ????
It is possible - but chances are not good.
Incidentally getting a taxi for £100($200) for a 65 mile trip on a Sunday might be a big problem - I would think double that sum. New York cabbies have a lot to learn from their London cousins when it comes to ripping off passengers!