About dealing with frustration and heading off tantrums: the books etc. that talk about how important it is to acknowledge a child's feelings (separately from whether there's anything you can do to help) have always made a lot of sense to me. Here, where part of the problem is that your DD can't express her own feelings as well as she'd like, I expect it might be especially important. E.g. say explicitly, "I can see you're really frustrated that you can't get that last piece in." (And, the hard part, resist the temptation to follow that up with "but you will be able to when you're older" or similar - that's beside the point as far as she's concerned, she's frustrated *now*. If you want to remind her of that kind of thing, do it when she's not in the middle of the strong feelings.)
Beyond that, I don't know. You could consider using something like, PECS is it, the picture-based communication scheme that children with certain disabilities use; possibly if e.g. she often wants to ask for something she can't point to, letting her have a picture she can use instead to show what she wants might help. But I'm not sure (a) that that's a good idea (you wouldn't want it to be a substitute for her speech, and I'm not sure whether it might be (b) whether it would be relevant to many of your DD's frustrations. Maybe if there are specific signs she often wants to do and can't, it would work better to invent new signs that she can do?
