Heathrow to Stansted at midnight

I am in a quandry.
My flt arrives into Heathrow on a wed. night at 11:30pm (23:50).
I have a 8:30 flt the next morning out of Stansted.
I am having a very difficult time finding transportation that late at night to get me to a hotel in Stansted.
Any ideas?
An early morning option is a little more scarey - I dont want to get caught in traffic and miss my flt - so i would rather get to stansted in the night.
Is there a train I could take and then catch a different train out to stansted?
THX "Stranded at Heathrow"