Devils Advocate here. The goal is supposed to be what the child is wanting. And she is thinking about being done. Why would the goal be to keep her in? The goal should be to get her to a place where is at peace with whatever decision she comes too. And one of the options is being done.
Since you didn't mention where the blocks are, for all we know they could be across events. It could be problematic as she would be scratching multiple events.
I would think (actually really hope) the point from the coaches perspective, is by putting her back the pressure to get the skills will be completely off. So she has no pressure and can still train the skills and have to get them back and solid before competing them. I rather think of that as a good thing. And that is how the coaches (and by extension you) should be presenting, again at least I hope they would.
Also if the L9 coaches are reluctant to have her there, that adds further pressure on her. Why would she or you want to be in a group, who is not 100% on her side.
Perhaps its time for a meeting with the coaches to come up with a plan that works for everyone. For me it would be back to L8, perhaps add some new more difficult skills to that, continue uptraining L9 stuff. She gets it when she gets it. Once solid, move her back to 9. Just because they have never moved up mid season, doesn't mean that can't change. Or train with L9, don't compete at all until she has the skills solid, or compete L8 while training with the L9s.
At our gym which is small all the optional girls train together, they just have smaller break outs for skill specific drills and practice so we don't have the clique type thing of different groups and coaches for levels.
I don't know your child but my child went through this last spring at a lower level. She was L4, told she would be moving to L6. There was a lot of pressure on her to get her BHS on beam and lots of work on bars was needed. She was struggling and worried about getting the skill, not blocked but worried. For the first time we had tears about going to gym. She got the BHS but bars weren't there yet. She ended up hurting her wrist and had time off. Due to the time off, no level 6 for her L5.
I have to say for her, she is happy kid again about gym. It took her a bit to get her BHS back, and L5 gives her time to work on bar skills that are not ready. My kid is the type who wants the skills solid. We can see her skills getting better and she is a much happier kid then she was in spring.
Also from a being done level. We have had a few girls quit this summer. It was harder on the parents then the kids I think. I can tell you all the girls are at peace with their decisions. And they were variousl levels from 4-9.
I hope you daughter comes to a place that she is at peace about.