DoP plays correctly for me.
There are three possibilities:
1. The album you're testing has the channels reversed.
2. One of the connections from your DAC is flipped around.
3. Your DAC flips the channel assignments with a DoP signal.
It should be easy to test.
Add a Parametric EQ filter to mute the left channel.
When playing PCM, does the sound play from the left or right speaker?
When encoding to DoP, does the sound play from the same speaker, or the opposite speaker?
If both are playing from the right speaker, everything is set up correctly and that specific album has the channels flipped around.
If both play from the left speaker, you have something hooked up the wrong way round.
If PCM plays from the right speaker and DoP plays from the left speaker, something is very wrong with that hardware.
I think the last result is very unlikely, but if it is the case you probably want to either encode everything to DoP, or convert DSD to PCM on the fly instead of bitstreaming it.