Good that you recognize that the balanced output of the Yggy might be better than the SE. I understand your desire for an apples to apples comparison with the Oppo, but I think an equally valid comparison is "best" to "best". Certainly, if you are keeping the Yggy, you will want the best sound out of it.
Here is where I first heard of the difference:
http://tweakaudio.com/EVS-2/Schiit_mod.html
"2. If you are using the coax (single ended rca's) outputs then you need to take the single ended signal from the xlr connectors for much better sound. There is a summing circuit after the balanced circuits that is not super transparent. This mod eliminates this circuit. You can get or make adapters to use (you use just pins 1 and 2 and you leave 3 unterminated....important!). Another way would be to put xlrs on your cables that use just pins 1 and 2. Another even more transparent way is to hardwired (more on this later). This mod will make the DAC way more transparent and clear.....mucho better."
Enjoy!!