Yes, the sadly destroyed 
ZDT Jr does have pass-thru outputs; its warmth probably wouldn’t be a good match with the HD 650, especially if your DAC is warm or dark (in my previous posts I’d missed your source and headphone preferences); I opted for the ZDT Jr. specifically for use with the HD 800.
Thanks for mentioning the Bottlehead, I knew I was missing something (also the Auris Audio Euterpe, about which I know absolutely nothing), and I’m not familiar with the Hagerman, either.
Re. the Hagerman and the SW51+ I now have my weekend’s forum homework lined up! Thanks @ProfFalkin for this recommendation; it was also instructive and great to read your post a while back in the Schiit Audio thread comparing the SW51+ with the ZDT Jr. and the Lyr 3.