I agree with trying the other gyms if for no other reason than to know if it is just your gym that says "no team" for her.
For my now 11 yo DD, when she was younger, she wanted to be on team. DS was on team; but she hadn't been invited. I mentioned to her actual coach that she wanted it and I kept being told she wasn't ready. She ended up taking a cheer tumbling class that was taught by the gym owner. He asked her to join the gym's cheer team, no trying out, she was on if she wanted it. She said that she didn't want to do it because she loved bars and beam and didn't want to basically just do floor. He took that well and then looked a little confused at us and asked, "If she wants to do gymnastics, why isn't she on our competitive team?" I said, "Because her coaches have said she wasn't ready..." He said, "What?! No, she is ready. If she wants it, her practice starts tomorrow at X time." She moved to pre-team the next day (was the end of season, so couldn't go on the actual competition at that time). A few weeks later levels were decided and she was put on the higher of the two levels that the pre-team fed.
I guess that what I'm saying is that sometimes, you just haven't been asking the right person. You don't want to be a pest; but as a 4 year customer you should be able to get an answer for what she needs to do to move to team since that is what she wants. Now, it is possible that you aren't seeing what the coaches see and maybe she isn't quite ready for level 5 (I honestly haven't seen many rec kids, even 4 years of rec) who are able to do all of the level 5 skills (I see a lot who have the floor; but definitely not the bars...). Does she have her kip? Even if she DOES have ALL level 5 skills, she will have to do level 4 first since it is required. If she has her kip then ask why they won't let her do level 4.
I will also say that we have some gyms in our area who absolutely do say that the kids have to meet certain criteria from pretty young and if you aren't level 4 by 8 years old (at the oldest) then you are NEVER going to move to their JO team. It just isn't going to happen. They have other options available for girls who don't meet their physical requirements or who are older; but it will never lead to JO. On the flip side, we have some gyms in our area that absolutely will give older girls a chance. Sometimes it is just checking out all of the gyms. And honestly, a 30 minute drive just doesn't strike me as that big of a deal. I get that it is tough with your work schedules; but I bet that you could possibly set up some carpooling. But, I live in an area where you pretty much factor 30 minutes for even short drives.