My 22 month old (butter wouldn't melt) son is such a bully, when we attend toddler grps or get togethers he slaps and pinches other children. I remove him from the situation, get down on my knees at his level and tell him that this is unacceptable and if he does it again we will go home, he normally throws himself on the floor and has a paddy occasionally head butts the floor or wall. His bad behaviour seems to come out of nowhere (if it involved a toy I would understand) please help - in garden at present drinking a glass of wine and recently started smoking again - a stressed out mum xx (little man is having a nap at present - bliss) !!!!
my son now 4 was a biter especially over toys etc even now he still does it occasionally and like yours could be over nothing but i think he is remembering past wrongs done to him by other children and is getting his own back. i do the same routine as you - time out on bottom stair - just keep going and dont lose faith :-)