Our situation is a lot like Madden's. My son also started "late" and competed Level 4 at age 9. He also, like your son did very well, and did so throughout compulsories. The only issue, like the other poster said was when they changed the age levels and ages. Since my son was a May b-day, he was considered a year older than he actually is. The age cut off meant he would have been 11 competing at Level 8. Our old gym did not have a JD team and the coach basically didn't want to coach my kid anymore because he was "too old, and not good enough" at 11. So, we switched gyms.
Our new gym doesn't do Levels 7 and 8. They do JD instead for 2 years and then go to Level 9. Their reason for this is that it gets the boys on the Pommel earlier and lets them up train kids on events they are good on, and they can design routines around their weakness. This year even though my son is 14, he will be competing as a 15 Level 9, which means he couldn't qualify for Nationals, but he probably wouldn't anyway, so not a big deal. Last year at Regionals, the 15-16 Level 9 was a pretty big group, as was JD1. The questions I would be asking your current gym is if they have a JD program and how it works. Our JD's practice the same hours as the 9's and 10's, it is also not looked on as a lesser alternative to JO, its treated more as its own level. Some gyms do not offer JD, or offer it more as an alternative to kids to want to make gym their second sport, so if your son is thinking he's serious about it, than you want him in a strong JD program.
The only concern I have in your case is that the gym doesn't seem to have a plan or resources to move boys up. While there isn't a big difference between 4 and 5(except the dreaded kip) , there is a pretty big difference between 5 and 6. I agree with the whole "levels are meaningless" concept, but for whatever reason, USAG decided to put upper age restrictions on levels, which left a lot of kids kind of stuck in limbo. Before the age changes it was really common for boys to repeat levels for up to 3 years. But the current model assumes that you start competing Level 4 by age 8 (which for about half the boys is really 7), and that you don't repeat a level in order to make it under the age cut off for 8. I would also be worried that its only August and the coach says he doesn't have enough time to do the Level 5 routines. Since its compulsory, it shouldn't be difficult to look at the manual and say, OK, in 5 we do 2 back handsprings, and in 4, only one. Our kids don't even start putting their routines together until Nov because they are spending all summer an most of fall training new skills, and it sounds like you won't even be training the new skills.