Apologies in advance if any of these sound twee or unhelpful, just ideas.
You could try having "family meetings" once a week where everybody has a chance to air things which are bothering them and be listened to without interruption and then everyone tries to come up with a mutual solution. You can also share things you are proud of/pleased with and discuss future plans which affect everyone even if it's just planning a trip to the park or something (to make sure there's positive in there too!). To prevent talking over each other, have a rule that only the person holding the salt cellar is allowed to speak and they pass it on when they are ready.
Have some kind of generic consequence ready for when you feel yourself getting annoyed - banning TV works in this house but whatever works for you. Bonus points if it's not a battle to enforce. Yes, it is better to use logical/natural consequences/reasoning/preventing something from happening directly, but sometimes it's easier to have something to calmly threaten instead of losing it. Also praise for good behaviour, all the time. Just acknowledge it when they are doing things without conflict, they will take note.
Tiredness really doesn't help either - make sure you and DH are supporting each other in this, not engaging in "competitive tiredness" but instead offering each other naps, early nights or lie ins on the understanding that it will be reciprocated as and when the other needs it!
Also are you trying to do too much? Anything you can cut back on/simplify? A friend of mine gave me a tip for small children which is setting the day up to win, planning activities which are low-conflict rather than trying to achieve loads (or "do something nice") and getting stressed out.
Lastly the big one for me is actually trying to be aware of it in myself and if DS asks me to stop shouting for example then I try really hard to stop and apologise, admit I was wrong, and rephrase in a less shouty way. Doesn't always work immediately at the time
but overall seems to help as he seems to become more aware of his own shouting too.
Is the house big enough to separate fighting siblings into two areas/rooms?