OP, I have a 11yo who's autistic and a 5yo who's got some stuff going on too, albeit her profile is less clear at the moment. The single best advice I've ever been given is that "behaviour is the language of the child". Every single bit of challenging or unexpected or irritating behaviour will have some sort of underlying reason. When my kids wake up, they are hangry and thirsty and can't be rational until I've fed and watered them, no matter the hour. Could you leave a couple of Rich Tea biscuits / buttermilk pancake and a water bottle by their bed for a few nights, and see if that helps? Not fancy enough to be worth waking early for, but takes the edge off.
There's also every chance that they may be triggering and re-triggering each other. My two get on beautifully, but one needs lots of quiet indoor time and the other goes bananas if we don't get her outdoors and doing social stuff at weekends, so we divide and conquer or take it in turns to do stuff with each of them. It'll ease a little for us in the next few years as my 11yo introvert will happily safely and stay at home by himself for an hour or two, but we are four years into this pattern, and it works well. We really notice anxiety rise when we move away from it.
Another thought on birthday parties - they are definitely not fun for every child. DS does not go to all of the parties he's invited to, and I explain to the hosting parent why not - we've never had anything but kind acceptance in reply. At your kids' age, he found the start and end of a party hard, so we'd go 10 mins late and leave a little early - often just after the blowing out of the candles. That made it manageable for him. Even now, he loves the local Laserquest which is the venue of choice for his friends' birthdays, but the room they serve food in is very loud and he can't handle that, so we go to the laserquest bit then quietly slip away before the hotdogs and cake bit.
You said "nobody I know would let their child get up before 6am". If you compare your children and your parenting to what other parents choose to tell you about their NT children and their NT parenting, you will make yourself unnecessarily miserable. It won't even all be true! Parent your kids in the best way for them and you - your kindness, your adaptations and adjustments, your standards, your expectations, your compassion, your prioritisation - and they and you will be much more in tune.