As they've removed the offer quickly, they were entitled to do so. It does, however, raise the question as to whether they were right in deciding that the offer should not have been made21. Check that your son is in the correct admissions category and that the home to school distance seems about right.
Looking at your suggested grounds
detrimental impact of being placed into the 3 tier system (2 school changes in quick succession)
Not sure whether this will fly. I think it may depend on the appeal panel you get. But yes, I think there is an argument that two school changes like this will be disruptive. Also, you applied for a place at a secondary school, not at a middle school. In my view, they should have allocated you a place at a secondary school. This isn't the normal year of entry for a middle school, so I am not at all sure that they should have offered you this place.
all 3 of our original choices are halfway between mine & his Father’s home. The school we’ve been offered is a 40 minute drive for his Father in the opposite direction to his work, meaning our current 55/45 childcare split would be disrupted heavily and my son’s contact with his Dad would significantly reduce
I'm afraid that isn't really relevant. Childcare and transport issues are considered to be your problem, not a problem for your son. I would still mention it, particularly the impact on contact with his father, but don't spend too much time on it unless the appeal panel seem to be interested.
my son had a severe stammer when he started primary school. He received a referral and we also sought private support and after a good year or so his speech improved drastically. There are, however, links between stammers and stress and being placed in a school where he doesn’t know anyone and the above factors too carries risk here (his school are preparing a letter I can use in my appeal to validate this)
This may help. It will be stronger if you can get a letter from a medical professional saying that, in their view, his stammer will be adversely affected if he does not go to the appeal school.
For the school we had an offer withdrawn on, I will also reference this in that particular appeal as his best friend is going, my son was delighted to find out he had a place and this was also announced in school assembly. I haven’t yet told my son he hasn’t got in, he will understandably be devastated
Friendship issues don't win appeals unless there is medical evidence that your son has a stronger need than other children of his age to be in the same school as his best friend. I doubt the original offer being announced in school assembly will help, but it won't do any harm to include that.
In addition to the above, you should look for anything the appeal school offers that is missing from the allocated school and that is particularly relevant to your son. This is likely to be different for each of the three schools, so you will be making a different case for each of them. Anything you can find will help to strengthen your case.
I would also ask the LA whether the school he has been allocated is the school he would have got if they hadn't made the error. It should be, but there is a decent chance they have ignored that and simply allocated the nearest school with places available. If he would have got your third choice school but for the error, that is a very strong point in your favour when appealing for that school.