OP, I just want to give you a hug. I am a mum to be myself so have no experience but I have been on the other side of it, obviously.
As upbringings go, mine was pretty priveleged, parents paid for private music lessons, dance lessons, holidays in France every summer and for musical holidays abroad on our own when they could afford it, and they sent us all to uni, though that was pre tuition fees and we got small grants, so nothing like the financial nightmare it can be now. The crucial difference was they gave us money to spend based on what they could afford, and if we overspent, tough, we got jobs during the holidays to pay for anything else we wanted.
We were also made aware of the value of money from a very early age, and although both my parents worked full time, they retired reasonably early, and there is no way I could have sat by wasting money on things like gym memberships and protein powder if my poor Mum was knackering herself with three jobs to pay for them. I think your DS needs a major attitude shift and that is really hard to accomplish when you are so tired as it seems he is capable of ignoring your distress and carrying on doing what he wants.
It would be hard to cut off everything straight away but the protein powder and extra food for his fussy little palate need to go in my view. If you could afford those things on a normal wage then fine, but you can't, and you shouldn't have to work extra to satisfy his whims. Gyms can be a nightmare about getting out of memberships, so you may be stuck with it for a while, but you could say he needs to give notice or find a way to pay for it himself. As for the private tuition, having gone down that road, it may not be fair to just cut him off, but you could say it's until end of academic year only and after that, he's on his own as you will be giving up at least one of your jobs after that.
Please talk to him, explain how tired you are, that you won't keep working like is to fund him, that you need time for your own life and to pursue your own interests.
The key difference is between can't and won't. The plain fact is that I am sure you could keep killing yourself for years supporting DS but you shouldn't have to, so you need to say you won't. And then once you've made that decision, stick to it, and if he bitches and moans about it, ignore him.
I look back on the times my parents wouldn't pay for x y and z and to be honest, I do feel a bit like they could have helped us more sometimes, but I am eternally grateful for the fact that although they gave us a leg up by paying for our studies, they encouraged us to be independent too, making our own decisions and living with consequences if we overspent. All of us got jobs within a couple of months of graduating and were expected to support ourselves pretty much straight away.
Don't look back, whatever you do. It's really easy to feel guilty when you're so emotionally and physically worn out and blame yourself for not making him more independent and Yada Yada Yada. Don't. You've been hugely supportive to him so far but it's clearly killing you. Yes kids are your responsibility, but at some point they have to start taking responsibility for their own lives. It's fair enough to go to bank of mum and dad in an emergency, like, unexpected job loss or some kind of catastrophic unforeseen event, but only if mum and dad a) can afford it, ie, don't have to work three jobs to afford it, b) there is no ore alternative, neither of those is true in the case your DS.
And on the solicitor's letter, I can see how that would be tempting but bad idea. I would only resort to that if your relationship with your son has irretrievably broken down, as if it hasn't already, getting legal on his ass will certainly do it for you....
I really hope things get better for you soon. As for your DH, it would be better if you could present a united approach, but if he won't support you, that's his look out, if he isn't ready to cut the apron strings he will just have to be the one finding yet more extra work to fund DS.
Sorry this is so long. But I really do feel for you and how distressed you seem, good luck...