First, you aren't doing anything wrong, and your feelings of anger/hate are natural. Don't feel bad for having them, and don't blame yourself.
Second, whatever I, or anyone else tells you, take with a huge grain of salt. Every child is different, every parent is different, every situation is different, and there's no "one right way" to deal with any particular issue. What worked for someone else may, in fact, work for your child but might not work for you. You need to find the solution that works for your family and your child, and while I know you're willing to do what it takes, don't discount your needs or your family's needs in an all-consuming effort to solve his needs. There should (and will be) a balance - keep looking and trying until you find it.
That being said, Jet is at a stage in his life where he is going to be this way. He's pushing, very hard, at boundaries you've set in place to see where the boundaries really are. Not just the boundaries where you'll say, "please don't do that" but the boundaries where you'll actually take action.
Coupled with ADHD and the mental inability of children his age to remember something that's not repeated a bazillion times, and you've got a long struggle ahead of you.
I don't think I can give you specific tactics that you don't already know. When my children go through this we simply do escalation of punishments. Time out the first time, go to bed the second time. I think we've done holding less than 5 times over all our children, but we keep that option available.
But we've not had to deal with ADHD. We've got two clearly on the autism scale, and 5 that are, insofar as we are aware "normal" (whatever that means). So I'm not sure that I can help you much. But here's a few reminders anyway:
Time
Children who seem to be struggling with issues may improve with more time and attention from their caregivers, or even just watching them more closely. I've had a few prolonged issues (ie, hitting, biting, or even just undesired behaviors like sucking on their shirt) where simply being nearby and observing them during their playtime has resolved the issue. But it takes a long time, and you have to pay attention so you can say, "You seem to be getting mad. What is making you mad? Why is it making you mad? What can you do to not be mad?" when they start going down the path that leads to the undesired behavior.
Constant observation is impossible, but like potty training, looking for the advance signs of a meltdown and teaching them what the beginning of that path feels like, how to notice it, and giving them the tools to deal with it can sometimes help.
Consistency
Boundary pushing is common at every age, but it changes over time. Telling them what the punishment is every time they do something undesired, and following through every time, and being absolutely consistent every time will help them solidify the boundary. They may continue to bang against it, but in my experience it doesn't take too many instances (particularly if the punishments escalate) for them to decide that this boundary isn't worth pushing, and to try somewhere else.
If they start a new behavior which you haven't set a rule for, try to avoid simply picking a punishment out of thin air while you're still in the moment. If you can, discuss it with them and see if you can both agree to a punishment for that misbehavior when you are both calm, after some time. I've found that once apart from the situation that caused the meltdown my children are actually pretty hard on themselves, so this is an opportinuty to put things in perspective and choose a consequence that fits the problem. Hitting a sibling, for instance, might require them to play with that sibling, allowing that sibling to choose what to play (or for very small siblings, teaching them how to entertain the sibling and make them laugh).
While I focus on undesired behaviors and resulting punishments, this applies to sadness and other disappointments. Helping them develop a toolset for noticing and dealing with overwhelming feelings requires a consistent process and approach until they eventually learn to notice an impending meltdown and try to resolve it themselves.
Discussion/awareness
Talking things through with them after they've calmed down and the punishment (if any) is done can help both you and them figure out what happened when both of you are calm and can look at the issue from a different perspective. Yes, saying "No hitting! Go sit on the stairs", communicates that the behavior is bad, but they cannot learn while in the heat of the moment. Waiting until they've calmed down, asking them to express their feelings, validating their feelings, then asking them how they might be able to approach the problem and resolve their feelings without melting down will make a significantly better impact on their learning to deal with something than the punishment itself ever will.
As far as medicating ADHD, it is true that it's overdiagnosed, and overmedicated in the US today. That doesn't mean that your child, in your case, doesn't need medication.
For my part, a meltdown or two a week isn't an issue for me. If that's the way they want to be, we can deal with it.
If it's daily or more than one meltdown a day, and my normal techniques aren't demonstrating improvement, then I'm going to find and accept medical help. Keep in mind that this is also a very long, difficult process - which is why I'll try regular techniques first. You don't just put them on meds and expect everything to be good, you try out a medication, then observe the results, and report back. The medication is adjusted, and you observe and report back. Due to the workload of most doctors this can take a very, very long time, and during that time the child will continue to change as well, so it really never ends. Unfortunately a lot of parents want a "quick fix" and so doctors overmedicate, and parents never pursue adjustments or alterations as their child grows. At best the doctor might see them once a year and do a quick follow up, but it's rarely enough.
Lastly, no matter what else happens, express your love as often as you can to them. A hug as they walk by, please and thank you when you ask them to do something, "I love you" many times a day, etc. You're both going through a rough time, and reassurances that regardless of their behavior and your earlier reactions you still love them will be useful in the long run.