Puzzled by a client- I apologize for the novel

I have a client who is almost 7 years old. She scored borderline on all portions of the CELF. Her parents speak three different languages at home (to what degree, I am not certain) but her primary language is English, as she is not fluent in any other languages...however as far as I have seen, she does not have a solid model for English at home. She is extremely high energy (cannot sit for even 5 minutes without jumping/leaping/dancing) and impulsive but can be redirected to a task with firm, consistent instructions.

I am really struggling with nailing down and treating exactly what her core deficits are. For lack of a better description, she presents almost like a mild Wernicke's patient: rambling, off topic responses to questions (frequently, but not always), press of speech, lots of nonspecific language "this thing, that one" and paraphasia-like productions of words ("lecklice" for necklace, "turkle" for turtle) in the absence of any articulation difficulties. She often uses a sound or a pantomime instead of a word (the "beep beep beep clock" for alarm clock). Sometimes despite several attempts to help her clarify, I am still unable to figure out what she is trying to tell me, but she doesn't seem frustrated by this, and continues to ramble without attempting to repair or clarify. She seems to have some word finding difficulty sometimes and will communicate that by saying "I don't know that one" or "This one is hard to remember". She sometimes leaves out articles (mainly "the"). Although her test scores are borderline, the things I'm seeing in her expressive language are concerning, but I am not certain how much can be attributed to poor models for English at home and poor attention/hyperactivity.

I am having trouble setting goals for her because she is a quick study and meets them fairly easily with a few repetitions (at least she has done so for following multi-step directions, regular past tense words, and irregular plurals). She picks up on patterns quickly. The grammar carries over from one session to the next in therapeutic activities but I am not observing generalization to conversational speech. I am at an outpatient clinic and do not have the opportunity to observe her in the classroom setting. Her pragmatic skills (except for the ones related to impulsivity, like grabbing at things) are good and she is cheerful and participates well in therapy. She didn't qualify for services in the schools (sigh).

If anyone has any ideas, particularly with how to address:
-Answering questions concisely without rambling and extraneous details
-Weird paraphasia-like word productions, and
-Getting grammar structures to generalize to conversation once mastered in therapeutic activities

I would greatly appreciate it! I feel pretty lost on this one.
I'll be monitoring this post because I have this client in the form of a 3rd grade male. The only difference is that he is not a quick study and has a learning disability.

Based on what you've described, she's not a functional communicator, so it's a little hard to believe she didn't qualify in the schools. I could've easily made a case for her. But, some schools require a certain standardized score or percentile in order to qualify.