I had a very opinionated toddler. Choices only went a small way. I came up with a lot of other tools as well. For example, I would start to put on his shirt. His territorial instincts came out and HE wanted HIS shirt. "HA mom! It's MINE now. " Or I would put his shirt on wrong, or put it on a doll. He would "correct me", triumphantly beaming that he was smarter. I would race him with my getting dressed. ... sometimes none of it worked, so I put him in the car as is and dressed him in the parking lot. A little hassle, but much easier because he was ready - maybe the new environment, maybe the drive cleared his head. Dunno.
I also kept reminding myself to check if it really mattered. I am used to a certain order, or eating cereal in a bowl, but that doesn't mean that it's the only way to do it. Keep repeating to yourself "the goal is to get ready on time. Is this something that gets us there? Can it be?" If it doesn't matter, drop it - no matter how odd it is. It will be forgotten over time anyway.
Another thing about getting ready - sometimes I had to be out really fast. I would get myself completely ready. Get the car completely packed. Get the clothes and morning things completely ready. *then* get the little squirt up.
You may find that a few minutes of morning snuggles or a morning story - some form of concentrated attention that fills her cup up - helps the rest of the morning go faster.
One last tip is that I had an "emergency bag" ready. It had car food & drink, clothes and such so I could grab that and go from there.
update: One other thing I thought of. Sometime during the day when she's in a good mood. Sit her down with pencil and paper. Explain the problem and write it down in one sentence on the paper. Have her and you come up with ideas for solutions. Write them down. Pick an answer. Draw a box and write the answer. You sign it. She signs it. Even though she doesn't read and write, the written word is magic and helps the agreement to be more meaningful.
If for some reason it doesn't work, go back to the agreement, assess what went wrong, look at the ideas and come up with another plan. At the least, you are showing her the basics of problem solving and also of persistence.