???
I think there's some confusion here: either on my part, your part, or both...
There isn't any "balanced output that isn't a....4-conductor". Balanced means separate and isolated ground leads for each channel, necessitating 4 conductors.
The adapter you linked to is not for a "balanced output". It's for connecting headphones with a balanced cable to a DAP with a single-ended output (look at the male plug... 3 contact points means single-ended, or non-balanced). If you're looking to take a balanced output (say from the iBasso Amp8) and adapt it to headphones with a single-ended cable, that's a big no-no. And, you probably won't find an adapter to do it.