I’d think even suggesting moving schools was allowing an option of him not taking responsibility for his behaviours.
The problem sounds like it is lots of different teachers giving him detentions but being unaware of how many he is getting. They have clearly lost their effectiveness and don’t work as a sanction.
You need to arrange a meeting with his tutor/head of year/head of house and work together. If shabby behaviour persists it will have a serious impact on achievement at GCSE which aren’t far away. He needs to knuckle down now and you need to support that rather than consider him running away from the problems.
You need to be setting him up to succeed. You need his timetable and you need to supervise his packing each morning. If he’s rushing in the mornings and therefore just throwing everything in at the last moment, wake him up half an hour earlier or ensure bag is packed the night before.
You could ask the school for a mentor to be provided from a willing member of staff or sensible sixth former.
You should be talking to him, in detail about his day. Asking how each lesson went and praising where it has been enjoyed or he’s reporting good work/behaviour.
Try to avoid a continuous cycle of ever increasing sanctions but do have known rewards. No detentions this week - let’s go to the cinema on Friday. Sanction only the worst misdemeanours and don’t punish twice for the same crime.
Get him into a routine. Have a set homework time. Support him in doing well at homework so he receives praise in class. He shouldn’t need homework support in Y9 but clearly does. By support I mean knowing what his homework is, asking him how it’s going, making suggestions and providing ideas, showing an interest and have him work where you are so at the kitchen table, not shut away in his room on his phone whilst he does half hearted scribbling.
Have him dress the part. Make sure uniform breaches aren’t too excessive and won’t mean he’s singled out as ‘trouble’. I mean no shaven heads with ticks in the side, no shaven sides and foppish long fringes. Make him follow the rules.
Reduce screen time, reduce added sugars in his food, increase exercise with good sleep hygiene. No phone in bedroom or an hour before bed. No phone during homework time. Get rid or severely limit violent or high adrenaline online or video games.
Increase his home responsibilities so he realises he’s meant to be growing up. Cooking supper once or twice a week, loading or emptying dishwasher or washing up, doing laundry, mowing the lawn, valeting the car etc.
How’s his reading? If he struggles academically get him support and spend time on the basic skills to make lessons easier. Hard to understand history if you are not a good reader. Not understanding makes messing about more likely. You’ll have a better idea when you support homework as you’ll be looking at what he’s doing and teacher comments.
How are his friendships? Is he in with a group of disaffected, low aspiring lads? If so, manipulating his social contacts might be useful. Children respond to peer pressure and a group of high achievers are likely to drop a problem child pretty quickly. Don’t let him fall in with the wrong crowd. Restrict the ‘hanging about’ in a feckless manner after school. Add structure.