OP you are very resistant to addressing the fact she may be unhappy. I imagine this is because you are putting a lot of effort into making your blended family work and expect to see a return on that.
But she doesn't sound happy or settled at all to me - she sounds insecure, anxious and in desperate need of comfort and control, which she is getting for herself the only way she knows how in spite of the trouble it is getting her in - doesn't that tell you something about this, that it's so compulsive this normally well-behaved child just can't stop doing it?
What on earth kind of 9 year old gets their kicks out of following their parent around helping with chores? One who feels like the love they get depends on what they contribute, I'd venture. She sounds overeager to please. It seems incredible obvious to me she has abandonment issues as her mother doesn't want to know much of the time, and her father (who it sounds like she did not live with full time before you all moved in together?) has upon assuming the resident parent role delegated the vast majority of parenting to his new wife. This may be of necessity but that is an adult concern, and doesn't lessen the impact on her. If all that had happened to me I wouldn't feel safe or loved; I'd feel like a parcel being passed around because nobody wants to take responsibility for it.
You explain how well she has responded to boundaries and routine which she didn't have with her mother; this is a big change for her, for all it is positive, and she has had a LOT of change in a relatively short time - her parents breaking up, living with her mother, moving in with your family, a new half-sibling and 3 new step siblings, a new stepmother with a completely different approach to raising children who is so invested in treating all the children in the family 'exactly the same' she makes no allowance for the completely different environment her two step children are coming from. She has had no choice in ANY of this. Even if she is not actually unhappy with the situation she is in, the sense of powerlessness and insecurity must be very destabilising.
Even your protestations that you 'love them all exactly the same' and that the fact they are not yours 'biologically' makes no difference, are actually quite troubling to me. You are NEW in this girl's life as a parent. She is new to you as a child. Your relationship is not, can not, SHOULD not be the same (i speak as a step child). It seems like you are really invested in your ideal of your blended family, and are therefore very intolerant of anything which goes against that ideal.
First thing I'd do is put all the snack food out of reach. That deals with the immediate problem.
Then I'd make sure her father makes some time for her. Alright you can't delay discipline on every matter for his two until he comes home; but this is not a live issue once the food is out of reach, it can be dealt with at leisure. So HE needs to spend some one on one time with her, talk about how she's feeling in general about her mum, her new family, and only when she's in a space to open up start talking about the secret eating. She's a child, SHE won't really understand why she's doing this or why she can't stop. He needs to help her draw those lines and alleviate the fears that are making her seek comfort like this. I think the best thing he can do is reassure her, explicitly, that she is going to be living with him for good, he will always want her, and he is never going anywhere whatever happens. She needs a strong attachment figure, it sounds like she has never really had the opportunity to establish that, and she is not going to be able to securely graft that onto you who she's only had in her life a couple of years. She needs to feel safe.
The other interesting thing in this is his second child. Are they much younger? How are they dealing with the loss of contact/residency with their mother?