The school are not entitled to deny your DS a full time education just because there was an accident in the classroom that hurt a teacher. It was unfortunate, but it wasn't bad behaviour and it doesn't indicate a need for a reduced timetable.
If he is falling asleep in class regularly you might consider if he would be better off on a reduced timetable, but it may well not be the best idea and it certainly seems unlikely that skipping mornings (when he is likely to be more awake) and going in in the afternoon would be a good solution for him (and he is the one who counts in this calculation).
You are suddenly talking about having him redo reception, but until this accident, it hadn't even occurred to you. So I think you should hold fire on that idea completely. Take a step back and assess how well he is doing. How tired he is when he comes home, how much he seems to be getting out of it, etc.
I suspect what you have here is a head who was desperate to appease a shocked class teacher who needed hospital attention (and I do understand why a head might want to do this, they value their staff and are likely worried about turnover and wellbeing) and in doing so they have not prioritised your DS's wellbeing as they are required to. Or even thought about what has really happened here and what the impact on DS might be.
I think you should go back in, armed with the guidance on reduced timetables and your DS's right to a full time education. Tell them that they clearly haven't been following guidance and that you would like to discuss why they think it is in your DS's best interests. Ask for documentation on any ongoing behaviour problems they bring up and if they can not produce any tell them that it is clearly not significant if they haven't bothered to record it and that you expect them to discount it in considering a reduced timetable. If they have documentation, ask them why you have been given glowing reports without this being mentioned. Also, assuming you do think this, that you think a less drastic intervention would be a much more appropriate response if they haven't thought it necessary to involve you up til now and that you won't agree to a reduced timetable.
Approach this with them as joint endeavour to find the best solution for your DS if you can. But don't give in the way you did the first time - you clearly need to hold them to the standards they are required to meet. Be resolute about them clearly evidencing what they think is best and why. Push back if you don't agree. In this meeting, consider only your DS, not the teacher's well being.
If they refuse to take your DS back, start an official complaint and get in touch with your local council to see if there is anything they can do to enforce your DS's rights.
If you haven't done so, I would consider helping your DS write a "Sorry for stepping on your hand by accident" card for the teacher, though if it's been several days already, that might look a bit too forced to be appreciated.
I would also start looking around for another school. This might be a glitch and they end up getting over the shock of a reception teacher having to attend hospital because a 4 year old accidentally jumped on her hand. It may be the start of them victimizing your DS (if not intentionally). They obviously aren't too on the ball with procedures and that's a worry, but you have no idea what other schools are like. And you may be the kick up the backside they need to get it together a bit.