I don't envy your position, but have faith!
Your intentions are good, and you are sensitive to their needs. There will always be a transition period.
One thing: don't apologise too much about doing things you have to do. I would announce things positively, rather than 'really sorry, another OFSTED requirement here, blah blah'. Our (lovely) head does this and it instantly allows people to feel put upon and stressed. It's your job. If YANBU, then it is their job, too. Being understanding and being apologetic are totally different things.
I sit on my hands during some of our head's addresses. He apologises and sympathises when we need him to galvanise!! Get them excited, get them aiming high, showcase good practise! (Can you tell I want him to use! More! Exclamation! Marks! In his speech?!) I sit with the rest of SMT some days, grinding my teeth because these targets have to be (and should be!) met, yet he is almost too kind and understanding, iyswim?
In short: I want to stand up and shout 'LEAD!!'
Am sure you are doing, but maybe check how you are asking for things? Total rant, there, sorry!!!
You'll be great x