So in your opinion, should I move onto more interesting math concepts, even though she hasn't fully mastered the stuff that "comes before" them? For example, she's solid with addition/subtraction of double/triple/whatever digit equations without any carrying/borrowing, but if it involves the latter she doesn't always remember the steps to solve them correctly, or makes mistakes when she mentally "groups" the numbers instead. Per her evaluation this all makes perfect sense, so I'm unsure what mastery will look like for her.

During her evaluation she was able to do things relating to fractions, measurement, time, and graphs, all <3.3 grade level and she's shown me she understands what multiplication is, though very early in that understanding. Do I just move on and not worry about mastering the carrying/borrowing stuff for now?

I feel like I’m answering myself now that I type it all out, haha.