Recommendations for next headphone

I have no clue what my Meze Empyrean driver type is but it sounds amazing with both my Benchmark HPA4 and Bryston BHA-1. I listen for many hours each night and now afternoons too (no 2 channel amp any more). I used to get fatigue and hated headphones about 10 years ago. I took a chance on the Meze and have been shocked at how amazing it is.

I am using the WyWire XLR over the stock cable, this gets the extra little bit detail that the stock cable did not get.

BTW - I am surprised you have not picked up the HPA4, given your stable of amps. I owned the DAC3 HGC at one time and the HPA4 is much better. Though I never had headphones to compare with the HGC, I am comparing the preamp section. I used the same components on the HGC as I am now using on the HPA4.

I bought the DAC3 to use as a dac mostly in a two channel system, but now am using the Naim and auralic streamer dacs. Also added the meze and hedds to the stable last night, so now to see what else to try. 

I'd throw the LCD4 in the mix if bass is your thing.  The Sony MDR-Z1R are very close in performance to the LCD4 and can be had for a lot less.

Last night I had a problem with my work. So I started some work at 9PM and finished at 5AM this morning. All that time I was listening to the Meze Empy with WyWire Platinum XLR. I was streaming the "1976! Songs of the Year" playlist on Tidal. It was so enjoyable that after I finished my work I stayed up a little longer listening to a few more cuts. This was with the HPA4 and DAC3B.

I love this headphone system.

I like Quads with Lavricables.