Sounds like it is doing what you want. Not sure why it will not play at 176 KHz, but 88 KHz is probably fine.
As to Direct Sound and WASAPI. Direct Sound uses the Windows Mixer which uses Windows built in software to resample everything to a given sample rate. It is generally viewed as a low quality resampler, compared to SoX. WASAPI (Windows Audio Session API) is a Windows audio system that bypasses the Windows Mixer, so the program (MC in this case) can send bits directly to the DAC without Windows changing anything. Most people use WASAPI to send what sample rate data is in the file directly to the DAC without any changes. That is called "bit perfect", since none of the bits are changed by either MC or by Windows.
Most DACs can accept many different sample rates without making any changes on the DAC. In your case, it seems (although I am not sure of this) that the 6i6 requires everything to be converted to one sample rate, like 44.1 KHz or 88.4 KHz. So, you need to have MC resample everything to that sample rate. It is better to use the SoX resampler in MC than to let Windows do the resampling.
Many DACs and mixers like yours use another driver system called ASIO rather than WASAPI. This is a driver supplied by the manufacturer. It typically provides for very low latency, which is an advantage if you are mixing signals. If you want to use the 6i6 as a mixer, then you should probably use the ASIO driver provided by Focusrite. Now that you have MC working with WASAPI, you should try the ASIO driver using the same DSP settings. As Jim suggested, the drivers sometimes do not work with 64 bit software, so if ASIO is not working with the 64 bit version of MC, then you might want to try the 32 bit version of MC. If you are not going to do any mixing, the WASAPI driver is probably fine.
ASIO drivers are also needed if you are going to send native sample rate DSD (2.8 MHz, 5.6 KHz, etc.) to the DAC. But, since the 6i6 does not support DSD format, this is a mute point. WASAPI is fine for the DSD converted to PCM as you now have it set up.