So far I've just dragged him away and calmed him down without hurting him.
That's what you should do, create enough distance that he calms down. Start doing/asking for behaviors he knows, heeling, sit, etc. Then gradually move closer. If he starts acting like "an idiot", move away again.
Across a Threshold - Whole Dog Journal Article
This bit in particular.
2. Over threshold is more than behaving badly. When a dog is over threshold it generally means that the dog is behaving in a way that we donít like. More importantly, it means the dog is in a state of distress.
When a dog crosses an emotional threshold, certain physiological and psychological effects begin to take place. The dog may breathe more heavily and his heart rate may increase. A dog who is over threshold is reacting rather than thinking; he is in a fight, flight, freeze, or fool-around state. He may not be able to listen to you (or even hear you). In addition, when a dog is over threshold, you cannot teach him to behave differently. A dog will not be able to learn until he back under threshold.
Honestly, I've never seen anything good come from the corrections being suggested.
The Dominance Controversy | Philosophy | Dr. Sophia Yin, DVM, MS
When you do train around the other dogs he was reacting to before, try to make it fun and upbeat. Engagement building exercises are good. Like this. The idea being to build a positive association to the thing that is negative to him right now.