I have a bottlehead crack, schiit lyr, O2, and Matrix M-stage at my disposal so hopefully amplification won't be an issue.
Oh, let's keep the budget under $400 used or new.
Not sure that any of those are in the same league as the LCD-2 or HE-500.
That, and the DT880s are Open; and the OP is looking for Closed cans.
I highly recommend the Sony MDR-7520.
(The top of the line in their Professional Series.)
IMO a better sounding - and better made - headphone than
the K550, AD2000, and SRH840.
Mr Speaker Mad Dog with Alpha Pads.
Alpha Dogs (over budget).
Denon D2000 / Denon D5000 (discontinued)
JVX DX700, JVX DX1000