... from the what would you do department.....

I'd get out a continuity meter and see what kind of jack's I'm dealing with.
Are there combo XLR/TRA like pro gear or what?

Correction
Are they XLR/TRS?

The inputs on the amp are called combo jacks......that is, there are 3 holes for the pins of the XLR and in the center of the 3 pins, there is a hole which accommodates a phone plug (TRS).  

It’s hard to say exactly what the problem might be without more knowledge about the design of the amp and the special cable which apparently is used to connect to it, but I suspect that it is related to some combination of three things:

1) You’ve gone from 300 ohm headphones (which were "rewired for balanced operation") to 9 ohm headphones (which have not been "rewired for balanced operation").
2) The headphone amp is dual mono and balanced.
3) The ground part of the phone’s TRS plug (the "S" in "TRS") is common to both channels.

So you may be either shorting one of the two signals in the balanced signal pair that is being output on one channel to the corresponding signal on the other channel, or shorting signals from both channels to ground. Or both. And you may be doing it through a much lower impedance than previously. As I said, it’s hard to envision this precisely without having more knowledge of the design, but I suspect the explanation is along these lines.

The bottom line: I suspect it would be a good idea to return the SE846 if possible.

Regards,
-- Al