I had to read this a few times: you use a $20k pair of interconnects from the DAC to a $450 headphones amp (to make it worse, balanced runs that you need to use adapter plugs with), the quality of which you describe in, erm, excremental terms. Did you deliberately choose to do that for a reason that I admit I can't think of? Sorry if I appear impertinent but this looks like a complete and utter waste.
If you bought one of Stax's top notch earspeaker systems, say the Omega II phones with either the SRM-007 tII (tubes) or SRM-727 II (transistor) energizer, it would set you back $4k, peanuts in the context of this system and you could continue to use your Odins as they were meant to: balanced. Alternatively, since you're using different digital cable anyway, to keep the entire transaction largely neutral even if you lost half of the Odin's retail price, you could sell them and buy a pair of balanced Valhallas to use with the Stax energizer ($6k + $4k).
By the way, you could of course also complete your cable loom with Odin digital cable which have been introduced meanwhile according to this site
http://www.highendcable.co.uk/Nordost%20ODIN%20Digital%20interconnect.htm
I have no interest in or affiliation with this store but have included the link since on Nordost's own website they are still not in the product descriptions
