Hi eyepea
I travel quite often at night (7PM to 10PM) and early morning (3AM to 6:AM) on the Puttalam-Anuradhapura road.
Elephants are not often on the road but generally they can be seen somewhere between the 7km to about the 10km posts before Karuwalagswewa, and again between Thabbowa tank and before Saliyawewa.
I have observed that these elephants are rather shy and I have had no issues. They are either on the side of the road or beyond the electric fences.
By and large I avoid travelling between 10pm and 3am, not so some much because of elephants but because of reckless bus drivers.
I don't advice speeding in these areas (clearly road marked as elephant crossing areas) because should you suddenly encounter a lone bull or a herd, you may end up hitting them. I travel at a speed where I could easily control the vehicle in case of an emergency.
Ekendra