LM4592
OPA627
AD797
OP604
My favorites were the Burr Brown 627 and 797, the OPA627 is warm and I liked it in one of my Headroom amps (can't remember which one), 797 was cleaner in my application (ibasso) the LM4592 is a runner up though, took a while to get a socketed DIP one, but it was worth it, it's very clean, almost to the point of desktop amps...
OPA627 sounds like it might be what you want, although the LME you're using now is pretty good too, it'd spec'ed very close to my LM4592, I haven't heard it before though
All of this was done on an iBasso D3+ and M-Stage with various expansion boards from Audio-GD, and my Matrix Mini-i which feeds signal via two AD1955 DAC chips (balanced), to whatever choice of Grado I'm using for the day or my HD580's