It's not uncommon at this age to go through this phase and I do give time outs when it happens but I do it slightly differently than you.

Any intentional hurting I have zero tolerance for and so, I'm more of a sharp action then I normally ever take which shocks them because it's rare. It gets their attention and it's clear.

I instantly say "No" in a firm voice. I pick them up and I put them on the time out chair. No discussion, no explaination, no reasoning. Only after their time out do I do what you do - down to the child's level and clearly and directly state that "we do not hurt our friends". Every.single.time. Intentional hurting is the only thing I give time out for with no redirection first.

You also need to get the parents on board if you have that relationship with them. Consistency is going to be key in making this lesson as short as can be. Explain to the parents that because it's now becoming an issue with children being the target, that maybe they could also agree to do the same at home.