This is exactly it, IMO. I'm also autistic, and I liken this sort of problem to being in a shop.
If there's one person in the shop right in front of me, I can hear them absolutely fine and we can carry on a conversation. If the shop's full and everybody's talking, I can no longer hear the person right in front of me because it's like all the other sources of noise (people) are screaming for my attention at the same time.
Similarly for a multi-step problem, like the fact that we've needed to redecorate our hallway and landing for three years. The problem is that just painting it will look crap because the plaster also needs doing, and the woodwork needs replacing, and we need to make covers for the weird stone skirting downstairs, and the stairs creak so I need to replace those, and the carpet needs replacing upstairs, but some of the floorboards also need sorting so I need to do that at the same time, and the banister needs to be replaced, but the dogs have been chewing the end post, which runs all the way through the floor to be part of the cupboards below, so they need replacing....
So the decorating hasn't been done, because my brain explodes with the magnitude of the task that was - originally - just refreshing the paint, maybe a two day job. It's basically now a whole-house renovation in my head with a whole bunch of unknowns.
It's exactly the same with multi-step maths problems - the steps aren't second-nature in her head, so they're big scary unknowns, which means that even if she knows what they are when prompted, they become an even bigger scary unknown.
My advice would be to...well, I don't know the specific set of problems, but let's say it's a four-step solution. Practice the first step loads with her to the point where it's trivial for her to do, then set her a bunch of questions that need both the first and the second step until she's got the process set in her head. Then the same for the second and third step, and then put the first three together, and finally the fourth step. Importantly, try to let her sleep between each iteration, so her brain has a chance to integrate it into her "this is natural, I know this" operation (I have no idea why this works, but it always has for me).
It might seem like a really long-winded way to go about it, but it might have a better chance of success than just showing her the process and saying "Do it!".