I don't care enough to google, but if this dac1101 isn't actually a headphone amp, but something you're just using to drive headphones, then I could see impedance mismatch being a real problem. Try plugging an appropriate amp between the dac and the headphones, and see if that solves the problem. Or buy jh13s.
I don't have an opinion on which carrier people should use, but if you're on a grandfathered plan, and they tell you "the new one is just as good", they mean "it's just as good, but it has a clause where we can change it, unlike the one apple forced us to give you years ago"