Well no, it doesn’t sound normal. It sounds extreme. I can see why you’re thinking about ADHD or ASC or some such. 
I dunno what you should do but here are some random thoughts in no special order.
I never restrained my DS because I couldn’t. If I couldn’t keep him in his room I’d walk away. I couldn’t ever talk my DS down, my attempts only ever made him worse, he had to self-calm. I see nothing wrong with putting a locked door between you and him if that’s what lets him calm down fastest and most safely. It’s not about winning or losing.
If you’ve been talking to polter then I guess you’ve already looked at “Explosive Child”? Your DS doesn’t sound exactly explosive-inflexible but some of the de-escalation techniques and “baskets” might help.
I think he was semi in control, because he held off picking up totally hard plastic/glass/metal objects and instead went for bits of cardboard which he'd emptied out of a recycling bag.
Well that’s good. The idea is to keep his self control. What would have happened if you had let him chuck the cardboard around without reacting? Would it have escalated and he’d have started throwing dangerous or fragile things, or do you think he would have blown out and calmed down in the end? Again, it’s about what’s safest, not who wins.
My nephew who’s a bit ADD-ish used to chuck things round his room, smash a few, then tidy up again afterwards, until he was quite old. My DSis let him get on with it.
If you can’t make your DS do stuff then don’t bother. If he wont eat before you go out then put a bread-and-butter sandwich in your handbag and off you go.
By all means have a daily routine. That’s reassuring to (most) anxious kids. Do you have a daily visual timetable for him so he knows what’s happening when, and when he can go on the laptop etc? My DS found those very helpful. And I wouldn’t worry too much about diagnostic categories. Mix’n’match whatever works. I had to do a lot of temper management with my DS who’s diagnosed as Aspie; he had a lot of anxieties; neither PDA nor Aspie fit him perfectly.
My DS had good phases and bad phases. Sometimes due to anxiety from new situations, changes at school etc; sometimes just adjusting to growng up. When he was doing well we would be more flexible and do more interesting varied things but when he was going through a bad phase we would avoid new things and get the timetable out and keep to a very regular routine again. When he was doing well we’d pick him up on more minor behaviour; when he was in a bad phase we’d let minor stuff go and just stick to the basics. Try not despair – a bad phase will likely lead to a better one.
“And mentally, I'm going why don't you get this yet? I've never given in to screaming violent tantrums ever.”
Right enough.
I didn’t give in to my DS’s screaming violent tantrums either. But I wouldn't refuse to give him something just because he was having a tantrum if you see what I mean. And I did let him ask for things in any way he could, no matter how snarly and rude, because he seemed to have a specific difficulty around asking for things he wanted. Asking nicely only came much later.
The distinction between tantrums and meltdowns has never been useful for me. Sometimes DS would stop a tantrum in an instant if I could give him what he'd wanted. But that didn’t mean he had been in control of himself. It just meant the utter uncontrollable frustration had stopped.
I did a lot of tantrum prevention, including trying to make sure my DS could have what he wanted as soon as I knew he wanted it - though my DS was different, he didn’t do all this “silliness” so I don’t know how to stop that. And it’s OK to say “Well, when you are very upset I will always try to give you want you want. But I might not always be able to”.
I said no and he stamped his foot and made a "HMPH!" sound like a toddler. And then immediately said "Oh no actually it's fine".
It's like the reaction is there so fast I can't pull him back from it or pull him up on it and then as soon as it's happened it's gone but if I say "I don't like the way you said that" then he gets all attitude-y in response.
You could ignore his first impulsive response and only react to the polite thing he said afterwards – that reinforces the good behaviour. And after all, how snarky would you feel if your boss kept commenting on errors that you had already redone correctly? 
I would be tempted to try to get him assessed asap. Parenting shouldn’t have to be this hard, not even in the school holidays!