I have an excellent recommendation! Call Beni at 052 859 5599.
He's a taxi driver with a van that seats about 13. He's originally from
England, so native English speaker, and he's very nice.
He's based in Modi'in, and regularly does the middle of the night
airport run. The Modi'in list has many, many posts -- including my
own -- about how great he is and how alert
and cheerful and kind he is at obscene hours of the night.