What a great way to test out what's going on!
Now, you know she can do it, she just needs to train herself to do it too.
One thing that helped my ds was to practice reading it silently or out loud on his own (his choice), before reading it out loud to me. We did this only for his Emerging Reader's books and part of his first DITHOR book. I told him that his was a practice round, so by the time he read it for me, I could hear it when he had it down pat.
Now, if he starts reading and has made a bunch of errors in the first paragraph, I'll stop him and remind him to look at it more carefully and ask him to have a fresh start where he is really concentrating and reread it. I don't really care about substitutions like "a" for "the", or "wouldn't" for "would not", etc., as long as the errors are not abundant.
The other thing that helps him to read more carefully is to assign him to read about 2 pages out loud to me and tell him he needs to do it quite perfectly, and if he does, then he can read silently. If not, we read more pages out loud. In fact I still do this with my oldest 10 yo for his DITHOR book (he's always been my one to mispronounce words). I've told him that reading well out loud is an important skill to always practice some, and that if he can show me he's good at it in 1 or 2 pages, then there's no need for me to have him do it for 3 or more pages. This motivates them to do their very best reading out loud, and it also seems to carryover into their silent reading, as their comprehension has not suffered.
One other thing that has been important for the stage of reading you are describing is to make sure I've kept the readings short, so that they can focus on reading carefully with expression, rather than rushing to finish reading a bunch of pages. We usually keep it around 4 pages, reading 2 aloud and 2 silently.
HTH!
In Christ,
Julie
I am so glad this was the case for your little Emma!