My original post was a brief summary of the problem as of today. Here's the complete story FWIW.
I originally had a Zen Mk II and enthusiastically embraced the Sense App when it was released (was a beta tester). Through various versions I was always able to play DSD files. In July of 2023, I purchased two albums in WAV format from small, audiophile labels. One was at 176.4 kHz, the other at 192 kHz (apologies for the error in my original post, where I said both albums were at 176.4). Both of these gave only loud white noise. I went back and forth with tech support about this and sent a sample track from each album for testing. Sense update 2.5.1 seemed to fix the problem and I was able to enjoy both of these albums and my DSD albums.
I have been diligent in installing Sense updates when they become available. As I first noticed the problems in the original post in early May, I assume that they are related to an update later than 2.5.1. I had been using the NDS/NDX profile; Nuno suggested that I try the NDS v2 profile. To get this to appear in the profile list, I had to reboot the server. At this point, my Zen Mk II decided to stop functioning. I replaced it with a Zen Mk III. I've tried both the NDS/NDX and NDS v2 profiles; however, the problems described in the original post remain.