The bad news is there is no quick fix for any of this. The good news is there are options.
Occupational Therapy has shown promise for us. In the last ~9 months we have seen improvements with our kiddo who too struggles with SPD, and in many of the same ways you have shared.
We are now starting play therapy as well to help get ahead of the anxiety and are working with a therapist that can give our child tools but also us, as parents, tools for the 167 hours a week they are not in therapy.
Find some coping mechanisms that work and roll with them, even if you don't love them. We didn't love bringing a tablet with us to appointments (we like to minimize screen time) but plunk on the headphones, turn on some music and that helps distract them enough for you to talk with a doctor.
Transitions are hard for us as well because they are generally compounded by picky eating. We don't fight the picky eating but just know that if we are all having takeout for dinner, we are probably going to be putting on a pot of water to make pasta, or a pb&j because it works. We always carry snacks and bring favorites with us, even to a dinner party to stay on top of the hanger as best we can.
Sleeping, for us, has has gotten better. Physical activity helps, we have trampoline that takes up a 1/4 of our back yard and its worth the annoyance. But I usually am in the room, at the foot of the bed laying down for our night time routine and that works. A lot of times, for us, we need a midnight snack and then settling back in is no problem, but we had to figure that out as parents not get inputs from our kiddo on it. Blackout curtains, setting the AC low and setting the bedroom up for sleep success have helped.
We have found, for our child, that being in nature is also helpful and helps center them and get them out of the hustle and bustle of the city a bit.
Routine also may help.. the transitions become the norm and then are not unexpected and can help to mitigate those metldowns.
One constant thing we need to remind ourselves as parents is to not fight it or punish them for not aligning with your expectations, its not a behavior issue its they are jumping into that fight or flight lizard brain response for things.
Before you turn down that promotion it may be worth talking with your prospective boss about your situation. If you are just starting to go down this journey with your daughter don't think its never going to change or get better.