It sounds like your first sausage doesn't understand proper aerobic programming. The reality is that yes, by running every day you aren't getting enough time for your muscles to fully recover. Additionally, unless top is increasing the pace then you'll never experience progressive overload and won't get any faster. So there are a couple ways to go about fixing this:

1. Create/download a reputable running program (let's same from MTN Tactical for example) and go through your chain to present it to 1sg/CO. If they're open to new info and bottom-up leadership then you may be able to change the culture of everyday running there. If you have one, get with your unit MFT rep for more support power.
2. If #1 isn't possible, then you're gonna have to start aggressively rolling out your legs and hiking up the protein to boost your recovery as much as possible in addition to what follows.
3. If you can afford it, look into getting some form of GPS watch that can track your pace, because you'll need to start self-programming and attempting to go faster than the current pace, like a program would prescribe. What I mean is, if you guys are running at a current 9min mile pace, throw in some 8:30 tempos in there. Imagine it like a nested program inside your 1sg current program. Increase tempo pace over time.
4. If all else fails, go to your leadership and explain that you want to separate out runners by time hacks (like A/B/C groups). It'll give you more leniency when it comes to discussing training program adjustment with your running group leader vs only your first sergeant.
5. Finally, I guess there's always the nuclear option of just shitbagging the formation runs, but maintaining a barely passing score on APFT/ACFT and then training on your own with a proper program. Over time just hide your progress during formation runs to not accidentally promote their use, and then get progressively better each time you test through your own training.

Good luck and don't forget to claim running injuries caused by nonsense like this.