We have three rescue dogs as well, in addition to a coyote problem that backs up to a mountain/city park. Two of the three are Chihuahua mixes that have exceptional hearing in the dog world.
I think I see your dilemma; the dogs have been home all day, you come home, they want to be around you no matter what, you have to exercise while dialing up the volume, dogs would rather be around you vs leaving the room - even if they are in discomfort.
Did some reading on the Internet since I've had similar questions and this is what I found:
1) No formal studies between loud music and ear damage for dogs, but...
2) Naturally, working dogs exposed to a loud percussive noise (gun shot) can cause temp and/or permanent damage - so it does and can happen
2) One vet recommended 70 db and lower
3) Signs of distress include licking lips, putting ears back, panting or yawning
4) High frequency sounds can cause discomfort/anxiety, but it's the decibels that will naturally cause the damage
I'm not into headphones either. Unsure what options you have. I do notice that my dogs will leave the room if really start pushing the volume on something I like, but I usually listen well after their excitement of seeing me has drawn down. Like your dogs, they usually won't leave my side unless we go through the daily routine of play/exercise before dinner in the evenings.
I found this small thread from 7 years ago that kind of mirrors our experience: