I'd personally recommend the Sony MDR7506. Best price and they sound awesome... They may be a little long in the tooth but great value! Sony MDR7506 Professional Large Diaphragm Headphone https://www.amazon.com/dp/B000AJIF4...ag=hawk-future-20&ascsubtag=UUacUvbUpU5616800
Good low budget headphones and it appears they would trigger the high impedance DAC but I'm not sure the cord is removable and not phone friendly.