If you're in a position where you can bandate (band mandate) then you have to take what the schedules and winds blow you. You can't just not teach a kid because they show up late. You can't decide to not teach a kid because they move in in January. Can an ELA teacher just not teach a kid when they move in mid-year? What if they're a refugee from another country, and haven't had formal schooling in six weeks - or ever?
Demanding that they come to extra time outside of class to earn their grade? That's not differentiating or scaffolding, and your admin will hammer you for it, and rightly so.
Finally, how the heck can they be "so far behind" only three or four weeks into the year that you can't get them caught up? If they're being dropped into your advanced class, ask to get them moved to a beginner class. Problem solved. If that won't work with their schedules, then it's up to YOU, the TEACHER, to figure out how to teach these kids WITHIN the boundaries of your class period and get them caught up. (Hint: Nearly everyone can learn to play a saxophone, drums, or euphonium decently within a few weeks if you give them the tools)
Service ALL the kids in your program, not just the ones who make it easy. Yes, it requires more work on your part. Yes, it's difficult. Yes, it's stressful - but this is what you signed up to do, and the cards that are on your table.