I'm a teacher, and I've worked in some really tough schools. I've dealt with behaviour that is off the wall. I know all the standard strategies. But I find that the tougher I get with my youngest the worse he gets, the more destructive, damaging and frightening. Consistent, immediate consequences mean nothing to him.
As you say "tough schools" I would guess secondary schools? Teenagers with challenging behaviour are a very different kettle of fish to young children. Commonly with challenging behaviour at any age, there is an element of developmental or communication delay, which in an almost-4yo, might mean some of his skills (communication, social skills, ability to handle change of plan, emotional regulation etc etc) are closer to the level of a 2.5yo. It's very unlikely that a teenager with any element of their development being closer to a toddler would be in a mainstream school - they would be in a special school. Even an 11yo with the emotional development of a 7yo would be starting at a very different point to a struggling 3/4yo, which is probably why they tend to be more receptive to those techniques of behaviour management. Being tough only really works if they CAN do the thing you want them to do, and they are choosing not to because it's more rewarding to them to do the disruptive thing.
Similar to how, if you can't speak French, it doesn't matter how "tough" someone is on you, it's not going to give you the ability to speak French - if he doesn't currently have the skills to behave in the expected way/handle the adult expectations, no amount of consequences are going to change that. It's going to take a combo of support/accommodations (in the language analogy, translators, simplified French, diagrams, or someone speaking English to you) and skill building (ie learning French - which takes a lot of time, effort, practice, and will involve a lot of errors at first).
Obviously it's not as simple as saying ah right he can't speak French - it's probably a more complicated combination of e.g. social skills, communication, emotional regulation, impulse control etc. - which is why it helps to get input from a professional e.g. SALT/OT, because they can tell you where he needs more support/input, and often how to develop those skills as well.
Yes to hearing and eye tests as well, that makes sense as something easy to rule out and likely to be accessible without such a long wait. You could ask the GP if they would recommend any other tests as well e.g. allergies, vitamin levels - but they might not in the absence of other symptoms.
You can check some stats on Scotland CAMHS waiting lists here: https://publichealthscotland.scot/publications/child-and-adolescent-mental-health-services-camhs-waiting-times/child-and-adolescent-mental-health-services-camhs-waiting-times-quarter-ending-june-2025/
An assessment for things like ADHD, ASD, etc is helpful but probably won't give you much practical you can really do in the short term, so IMO it makes sense to stay on the NHS waiting list for these, and prioritise services which actually offer practical follow up if you're going to pay for anything privately. Obviously there is medication for ADHD, but it's not usually recommended in children this age anyway. If there is a way to go directly to any other services such as speech/OT, then it sort of makes more sense to do that, and only look into the private assessment route if it turns out access to some kind of therapy is totally blocked off unless you have a qualifying diagnosis.
We just need to find ways to deal with the switch, where he just seems to flip to being out of control.
As I recommended before, I would highly recommend Mona Delahooke for understanding this shift, and the book Big Baffling Behaviours (by Robyn Gobbel). Stuart Shanker's Self-Reg is also helpful, but I think as a supplement to other things. Gobbel's book is good because she lays out about three or four different "levels" of this dysregulated state and the signs that she lists as being indicative of having moved from one to the other were very helpful for me as my DS2 (age 7) displays several of them. However this is very much aimed at parents rather than teachers. Conscious Discipline has similar aspects for teachers - their videos are good and worth pushing past the cheesy/dated feel.
It may be worth the preschool asking whether there are any resources they can access through Local Authority funding or national government funding in the areas of either behaviour support, emotional regulation, or social/emotional learning (SEL) support because there are lots of general programs aimed at settings to use to help children in their care. I am abroad, but my child's Kindergarten recently purchased one of these programs to help some of the children in their group and they went through it with all the children, including my just-turned 4yo, who doesn't particularly struggle in this area - it was still helpful for him. They are usually designed to be fun and appealing to this age group and include things like songs and stories and characters to explain the concepts. If they already have access to something, it can help as you can use the same language at home.
For example this link is for practitioners and it is valid in Scotland as well as England and Wales.
https://birthto5matters.org.uk/self-regulation/
You could also try keeping a sort of diary over a few days, and get preschool to do this as well (or ask if you can go in and observe him, if you can do this without getting too closely involved) - if you can write down things like body language signs that he seems to be getting into a more wound-up state, as well as what he is doing/what's happening around him when he's more or less stressed, you might see patterns here. You might also see patterns in what kinds of experiences for him tend to trigger the outbursts, or if there is a pattern e.g. in the time of day it tends to happen (which might suggest hunger or tiredness as triggers, or discomfort from needing the toilet) And notes on what sorts of activities seem to help him come back to a calmer place too. Even if they seem counterproductive or not ideal, I would just write it down for now because you're looking for patterns.
Common things IME which might be worth looking for are things like:
Sensory stuff
auditory - what can you hear, is it loud/quiet, are there lots of conflicting noises, how are people speaking, are there irritated/frustrated/stern tones vs loud and enthusiastic vs calm and soothing, quiet music vs loud, background noise like traffic or the hum of a fan etc. Does he say things are too loud, or put his hands on his ears at all or want to wear a hood/hat when it's not cold?
visual - is there a lot going on at once, are the colours bright and clashing vs calm and muted, is there lots of moving visual stimulus, are all lights bright, does he seek out dark/cosy spaces? Is the room big and open vs smaller and more contained.
smell/taste - are mealtimes a trigger, are there smells like food cooking or toilets or perfumes or strong-smelling cleaning fluid?
touch - does he struggle with clothing textures, is he bothered by getting his hands wet/dirty, does he avoid or seek out messy play, or seek out textures? does he want to have his shoes or coat off/on when inappropriate? Does it bother him when other people touch him? Is he always trying to lie on people or be "squashed" into small spaces? Does he chew things?
Movement/exercise (proprioception) - is it better or worse if he's had an active day vs a more sedentary one, what about movement like spinning/swinging, does he tend to seek this out or dislike it?
Discomfort (interoception) - does he go to the toilet when he needs to vs waiting until the last minute, does he recognise when he's hungry/thirsty/hot/cold or seems to run more hot/cold than other children?
Then you've got:
Emotions - is he getting derailed as a result of strong emotions? Is there a pattern around particular emotions? How do the adults around him (incl you) tend to deal with this?
Demands/control - does he seem to struggle when someone else asks something of him, are there any situations when this is OK? Does he tend to try to control others? Does he try to enforce rules with other kids or speak to adults as though he was the adult and they were the child, without recognising this is seen as "cheeky"/defiant?
Familiar vs new - does he struggle with unknowns/unexpected things/change of routine or plans, does he seek out predictable/familiar things when stressed out? Is routine comforting to him, e.g. does he play out "Nursery circle time" at home?
Social - how many people are in the room, does he do better in smaller groups or prefer to be alone? Is he misreading social interactions or being misunderstood a lot? Does he do better with adults/children/older/younger/boys/girls/animals?