I'll go out on a limb and ask, have you ever wondered if he's on the spectrum or has ADHD?
A good trick with kids who have the tendencies you've explained is saying, 'Stop. Eyes to me'. get on his level and get him to look you in the eyes. The language needs to be calm but firm. Really work on helping him to stop, then look at you, take a deep breath and tell him to "Listen". I find that holding hands helps. Make sure he is fully engaged before you speak. You almost have to 'train' him to stop and listen. The 'eyes to me' will really help.
He gets himself into such a flurry of excitement and it's overwhelming for him, I'm sure. You have to temporarily pull the plug, bring him back down (as if he's a helium balloon in flight, tug on that string and pull him back down to earth), and help him to find his inner calm.
It will take all of your effort and patience, but you can do this.
It's vital for him to find a calm space every day after a long day at school. Not much discussion. just quiet time. Brain rest! That could be just drawing at the kitchen table with really nice music playing. Kids' meditation. Even a calm programme on the TV. Just a space where he stops and steadies his fast pace for a bit.
The humming sounds like 'stimming' which is what kids on the autism spectrum tend to do to self soothe.
You may not be able to totally change his habits but you can help him to find a calmer headspace by using the Stop-eyes-to me-listen type of language. My son is like yours.
How does he engage when it comes to tasks? Is he into using his hands? I find working with kinetic sand and things like play-doh really calming. I know he's 9 but my 9 year old has a 10 year old friend who is ADHD. When she comes over, she plays for ages with the kinetic sand (we have moulds and cookie cutters which they use). It's very addictive and calming! Making slime (messy but worth it) is a really great way of engaging in something, using concentration for a sustained period, but at the same time, it's very calming and therapeutic.
I don't wish to diagnose your son in the least. But sometimes, the strategies I use with my own ASD son and with the kids at the school I work at can totally be carried over to the mainstream children. Some kids just need more help in finding their calm place.
He may benefit from running or something like gymnastics (less team sports and more 'running' based sports). Martial arts is great for discipline and feeling more centred.