Hey there! I am no expert, and I am training for my first princess, so perhaps I am not the best to answer, but I so feel your pain & your fear. So if that is anything, here goes...
You need to maintain the 16min/mile pace--period. You do get some cushioning if you can start in an early corral. The official "pace time" does not start until the last person in the last corral crosses the start. That is why some of the princesses finished with a more than 16 min/mile pace--they started before the last person who crossed the start. However, from reading all the posts from the veterans, the folks who got swept say that they should have trained for a 16 min/mile and didn't or underestimated.
Like you, my issue is not the distance, it is speed. I don't have a physical limitation except my own obesity. The laws of physics & gravity are not my friends...

Right now, my personal best for a mile is 18:52. I know I can't sustain even that for more than a mile right now. BUT we have 10 months to train!!! I am going to do my best. Celebrate what I can, register, and work hard every day to get my training in, and then let the chips fall. What I have come to peace about is that it is the training that is important, not the race itself. For the first time in my life, there is something that is motivating me to take care of myself and live a better life.
So, with all that, I am so sorry your hip is such a struggle. That totally sucks, and to be honest, I am not sure how I would deal, but likely not as well as you. I think if you can find any joy in the journey to the Princess then do it, but if it's just getting the tiara, then it's not worth it. I think a race is a lot like life in general...it's the journey, not the destination, that really matters.
Good luck to you. We will be here rooting for you no matter what!