I spent a great deal of time looking for a high quality headphone amp to use with my digital church organ. I'd allocated significant budget to this, and in the end bought one of these:
https://www.amazon.co.uk/dp/B017VXNL..._zD1JEb6X7059N
While they are oos on Amazon there are plenty available on eBay from various suppliers around the £50-60. They are superb with virtually no colouring of the sound or distortion. I can't imagine you will find a better sounding headphone amp and the price is extremely attractive.