We were very recently in the same position. My DD is almost 7 and has ADHD as well. She was diagnosed about a year ago. Soon after we found the right meds, she began thriving in all areas, and she suddenly LOVED gymnastics. She was practicing anything she could do at home constantly. She had been on a break from gymnastics classes for the semester, so in June I signed her up for rec classes at a very competitive gym (sounds like yours). Little did I know that this gym only took kids for pre-team from their preschool classes, and she had just moved to the 'big kids' classes. She was begging for more hours, so I let her go twice a week. On the first day of her second class, that coach pulled me aside and recommended weekly private lessons. He said he was sure she could make team at some point (I had not asked about that), but he needed to work with her to improve her form. Long story short, I did let her take some private lessons, and she REALLY shined in those times. One-on-one is great for any kid, but it's especially beneficial for kids with ADHD, because it eliminates the wait time that happens in rec. I posted about our situation in this forum, and I got a lot of similar responses to yours. Most people seem to be against private lessons, but not everyone is. I think your concerns are valid. It is very easy for kids to get overlooked at large competitive gyms. And some gyms DO take kids exclusively from preschool but not older classes for pre-team. Giving her private lessons won't guarantee her a spot on team, but it will help to get her noticed. Do what you feel is best for YOUR child.
As a side note, even with some private lessons, I don't think my DD would have been chosen for the pre-team at that big gym. They just had too many talented kids to choose from, and my kid was pretty unfocused from 3-6 years old, so she never looked like a natural compared to all of the other little ones in her group. Fast forward to now, and I decided to have her evaluated at a different gym (still competitive, but not so prestigious). After one practice with their pre-team, she was invited to join them. I talked to her rec coach at the old gym last week to let her know about that situation, and she was so encouraging! She said to definitely try the pre-team at the new gym, because if it was going to happen where we were, it would have happened by now. All of that is to say that sometimes the really large and 'elite' gyms make our girls look like a dime a dozen, and sometimes it takes a different environment to help them shine.
The best advice I got from parents in this forum was to really investigate and make sure you know all of your options. The 'best' gym is not always the best fit for each child. When I started really paying attention, I noticed that the team coaches at the elite gym were all very serious and intense. New gym has a much more positive atmosphere, and the girls look happy to be there. I didn't know them by name because I'm not in the gymnastics world, but after much research I found out that they have a fantastic program. None of this guarantees that my DD will thrive there, but at least she was given a CHANCE. I think that not everyone gets that mentality, but all I wanted was for someone to give her an opportunity to show what she could do and not shut her down before she ever got started. Good luck to you and whatever you decide! I'll be rooting for your little girl.