whoareyou - Your post confirms that at least some newer NVIDIA HDMI systems support 88 and 176 KHz sample rates. I had updated my previous post to reflect that. That support was added maybe 2 years ago. Historically, it was a known problem.
In general, Intel hardware with Microsoft drivers usually does not support 88 or 176 KHz over HDMI. I am not sure the new IRIS graphics system has changed that. It is hard to find information on the new Iris system, but it may not fully support 44.1 KHz multichannel.