This is YOUR chance to really SHINE! You seem to understand that what she is doing is going to make you better. It is her “modus operandi” that you and your staff object to! If you set yourself up as her “representative”, everything will go through you. She gives directives to you, you take them to staff and help them implement as a team (and soften the blow). By same respect you report to her and keep her in loop so she doesn’t need to talk to staff. You are the buffer! (Welcome to management). So when all this dust settles, the policies will be implemented, the staff will be happ(ier), you will be doing your jobs better, the patients benefit, and YOU look great as getting it all done without a mutiny! Remember you must believe in the changes and convey that to staff. Otherwise they will expect you to take their complaints about the changes back up the ladder. Your boss wants to see it get done with no grief. Make sure it happens that way! Good luck!

Yes, be the buffer; that’s what I was going to say.
When you’re dealing with staff, sympathize with them over her lack of people-smarts, and agree it’s hard to change so much so fast, etc. Then emphasize the pluses of the changes, once their made.
Also, tell them you’ll take specific reactions back to her — picking the strongest of their objections or suggestions.
When dealing with her, remind her that people can’t learn 1,000 new things at once, at try to get her to prioritize — what changes will fix things the most right away, can we put those in place first, then go after adding the others?
(Getting a sense from staff and your own experience as to what the biggest inefficiencies are will help.)
If you aren’t already in the go-between role, go to whoever is above her, and explain that, although her changes are sound, and you agree with improvement, that she’s not great at getting the staff with her, alienates people, and creates resistance — you’re afraid you might start losing good people, people are too stressed to focus on doing their jobs, can you help make the changes happen with less trauma.
You think it would work better, and be better for morale for her not to deal with staff directly, but go through the people between.
Then, when you deal with her, do raise the legitimate concerns of staff — if she’s truly detail-oriented, she will want to tweak things to take their feedback into account.
“It was pointed out to me that moving this there” (to invent a lame example) “would mean staff would be spending MORE time going back and forth; could there be another way that avoids that?”
In short, putting things in positive form, and keeping things specific will help.
The best managers do what they can to make it possible for the people they manage to do their jobs well. So that’s now your role.
Helping alleviate their anxiety (helping them see that, when they get used to the new ways, it will be better for them) after showing them you understand that anxiety.
“Changes are hard, and this situation makes us all anxious; but when we get this working, this WILL improve things for you.”
The letter of the law part is the hardest part, as it usually leads to insanity (when you ignore the purpose of the law, what you do usually works against that purpose).
I don’t know if she can be reasoned with here (such people usually can’t), but you can try: “Hmm. I thought the point of this particular policy was to …. In this situation, it seems doing exactly what the directive says would prevent that from happening.”
As I say, that’s the toughest part of the nut to crack. (I’m clearly a spirit of the law type, and have little patience for the Letter folk.) That might be the kind of time to go to a higher-up to see if the truly wrong-headed things can be over-ruled.
I’m a firm believer in getting the people effected involved in developing and figuring out how to implement change — not only are you getting the value of their better understanding of the nitty-gritty details of what they do, but you get their buy-in, the more they are involved in planning.
But it sounds like yours is a top-down situation. Unfortunately, most are, which is why low morale, high turnover, and incompetence and wrong-headed systems are all so common.
Well, hope this long ramble helped.