DD's teacher did call us into a "first concerns" meeting a couple of weeks ago, as there are indicators of ADHD/ASD. I understand actual diagnosis will be a long journey.
Does that mean that they've made the referrals yet? It is a long process but it's even longer if she actually isn't on the waiting list yet 
DD has zero road sense. This is very typical of a ND child. She's not doing anything wrong. You just need to keep her safe by holding her hand and gently going through what she needs to look out for.
DD cannot keep track of her belongings and never knows where anything is. Constantly losing things or leaving things behind. Again this is fairly typical. If she does have ADHD she won't think of things she can't see. You need to help her not leave things behind. Make a list with pictures as well. Yo do on her bag as a reminder and think of shelving it units on her room where things are tidy but visible.
If we ask her to do something - put shoes on, brush teeth, anything at all - she never does it the first or second or even the third time we ask - it almost feels like it has to escalate before she'll take any notice of us and actually do it.
Try making it a race. She will get zero dopamine from carrying out a task like putting on her shoes but time her and give her a fun challenge to see if she can do it in less than say 5 minutes and make a huge fuss if she manages it.
Attitude/temper - DD is always on an emotional rollercoaster. Highs and lows. Temper flare-ups where she'll snap and shout at us.
The Explosive Childd* is a great book to help you deal with this.
Constantly wants to collect things and be in control of resources, whether it's floats at the swimming pool, toys, snacks - DD wants to be in charge and give them out. I don't think she plays nicely with other children, from what I can see.
Not sure on that one sorry. Hopefully someone will be along soon who can help you with that 
We've tried everything - reward charts, stickers, natural consequences, punishments, removing toys/screentime/treats etc., explaining everything over and over so she understands . . . nothing works and the issues are still there, and getting worse if anything
All of these are great techniques to use if your DC are NT but if they are ND they simply don't work. The book I linked to earlier should help with behaviour.
Does this resonate with anyone? It really feels like every other child is polite and well-behaved and we've massively failed DD in some way
Yes and it can be hard. You're probably adjusting right now to the DD you have and that parenting is going to be different to what you expected.
Have a look at the SN Children Section. You can ask on there about getting an ECHP. She doesn't need a diagnosis to get one and they can give you information on how to obtain one and what it should include 