I loved your post suevv.
We lucked out when my DS was 4 and found a montessori style school that didn't force him into things. He didn't sit down at circle time for about 2 months, and that was okay. He eventually wanted to! It was the guitar songs that sucked him in.
It is not so much the preschool's stated philosophy but how the teacher handles the individual that counts. This teacher described his personality as "passionate" and complimented how he could energize the other students when he was engaged. She chose to focus on his positives. It was a lovely way to look at him as there were several other possible descriptions on any given day! They were so nice to him and had generous hearts and it went so far for him. He attached and bonded and respected them and the experience continues to serve him well now 2 years later when he is forced to do much more that doesn't quite suit him and gets so much less positive attention from a teacher.
So my first question is whether your DS is getting a foundation of school right now that includes feeling attached to his teacher, and his teacher feeling appreciation for him? Is she negative or positive? When you are there do you hear mostly comments that restrain him, or are those comments outweighed with positive comments?
At home part of your success with the 123 method may be that you also are often polite to him, compliment him when he does a good job, encourage him in a positive way, are friendly to him or give him hugs etc. You likely try to minimize the time spent in grumping at him by simplifying it to the 123. So the overall situation is generally stable and positive overall, right?
So that's the first question, is his teacher similarly spending most of her time with him in a positive way? If not, that is the biggest issue.
Next, is the teacher helping the other children respond to your DS? For example when he pushes them is the teacher intervening saying, "DS no poking?" or is she saying, "Matt did you want DS to poke you just now?" "How does that make you feel?" "Matt would you like to ask DS to keep his hands to himself?"
Some preschools do a great job of social scaffolding. And other otherwise good preschools don't. It may take observing to see what is happening that could be improved.
One preschool I saw always had the person who had accidentally tripped or whatever to another child go and get a cold pack for the child that had fallen down. It was great as it gave the child who had pushed/etc something to do while the teacher was attending to the one with hurt feelings, and the act of giving it was more tangible than a forced "sorry". They felt helpful.
But that was just one little part of their overall approach. The teacher would be literally down on the ground at child level. They would get the "hurt" child to explain their feelings. Everything stopped while the pokee or pushee got to say their side. The hurt child would typically say something one couldn't hear. The teacher would paraphrase "Matt says his feelings got hurt".....Matt is asking you not to poke him again." It made a lot more impact (at least on some kids) than a teacher intoning "don't poke" or giving them a time out. It was all very non-judgmental, nothing punitive or negative about it at all.
The negative or punitive responses were entirely saved for truly dangerous situations.
Probably a lot of your DSs behavior is the stimulation and a enhanced level of tension induced by perhaps him not being quite ready for boring circle times, feeling a bit pent up by the demands, etc. It's understandable and lots of kids are just the same. So if he is seeming to get a lot of negativity for it then it may be the teacher could use you observing that he responds best when another child tells him to stop, etc. Or however you can figure out to enhance their social teaching.