One thing strikes me, tiny... Because you're not sure what's wrong, you're stuck between two very different sets of reactions and courses of action, that do in fact (at least partly) contradict each other...
You say "he does need that shock treatment - hasn't a clue of how good life is at home" and the "tough love idea" appeals. (And I really do understand the appeal!) But if he is actually clinically depressed, then this approach is unfair and won't work. He doesn't need 'tough love', he needs counselling, and meaning/purpose to his life that he has found, and perhaps some kind of medication. Your DS may feel like you're judging him for moods he can't help. But if on the other hand he is being lazy and entitled, then 'tough love' might work. 
It's a very hard call.
You say you feel better 'doing something', so here are some practical ideas... :)
I notice you say your DH is home full-time and has the flexibility in his day to be able to do activities with your DS...? Then I suggest that they start the day regularly with some sort of exercise - whether it's a walk or run, a swim or a trip to the gym. Exercise releases endorphins as well as adrenaline, and is very helpful for depression. And if DS is up and about, and has had an energy boost, he's less likely to go back to bed/games console...
Also, I agree going back to the GP is a good idea. Ask for a referral to CAMHS. Meanwhile, I know someone who recommends this online CBT 'training programme' . It's free, might help him reflect on his feelings, and might give him a bit of support while he waits for counselling... It might even suit him better than counselling if (like most teenage boys) he's not fond of talking about feelings.
The website apprenticeship.org has loads of opportunities - I believe it has every apprenticeship in the UK. You can search by topic or by area/postcode. It might help give you (and him) ideas.
I second the idea of an FE college rather than school. A lot of kids find school does not suit them. My own son got into a terrible downward spiral from Y10-12, but is now back and re-engaged (mostly 
) in a BTEC course at an FE college. He says he feels like "the last five years were a total waste of life"; and personally, I don't think I appreciated how bad school made him feel until I could see him recovering his confidence and self-esteem, more than a year after he 'escaped'.
I know you will have pushed hard to get his school to agree to keep a place open for him, but really, I would seriously consider talking to your son about this, and withdrawing your request to keep the place open. It may be that the thought fills him with such dread that it keeps him miserable and depressed. It might be that if you 'freed' him from this dread and said, "OK, we can see that isn't what you want. You dn't have to go back there. But you do have to do something else" it would give him fresh energy and motivation.
I didn't find a 'magic wand' - last year was a nightmare tbh - and I think maybe it just takes time. It's very common for kids to 'waste' a year some time between 14-19 - there's even an extra year 'officially allowed' in free ft education, because it's so common!
Ultimately, I think kids need to find something - anything - that engages them and gives them a bit of a buzz. Once they do, they can put their energy into that, and just 'tolerate' everything else. :) But if they don't have that buzz, everything else just feels meaningless.
Last but not least, I also suggest that you make some changes. My first thought was that you sounded sad. If you think there's some truth in that, then I'd say you need to re-think your life and add something(s) that make you happy. Teens may seem totally self-absorbed, but actually, many of them pick up on it if their mums are unhappy, and it makes them stressed and unhappy too. Also, doing nice things for yourself - whether it's a coffee with friends, a new hobby, a swim, sauna, massage - whatever - will help you deal better with the stress of worrying about your DS!
Good luck with it all. :)