Ok, the moment of truth has arrived...
As
@Buckeye Amps mentioned, the board designer and I have been going at this diagnosis feverishly. Admittedly, should have found sooner, but I made a critical test error and (as mentioned) the designer had been plagued by a bad dummy load that obscured his measurements until just recently. Since I have been working closely on the troubleshooting, Dylan is allowing me to represent the team to share our finding. In the end, the designer found the cause.
And the culprit is...
The binding post connection tab.
Unknown to
@Buckeye Amps when he bought the binding posts, the tab is primarily made of steel. Steel is a relatively poor conductor and like a loose or oxidized connection can cause distortion. As with some others, I thought the culprit was the input board, but fortunately it was not. Honorable mention goes to
@pma.

Within his first few posts in this thread, he mentioned problems with ferrous materials in the signal path. We just had to find it.
Anyway,
@Buckeye Amps is working on lining up parts and plans to address this issue in customer units and his production. He will share more details soon. Both of us are planning corrective actions to avoid this issue recurring.
P.S. (for those wanting some additional insight, please read on...)
I mentioned a critical error on my part. Tbh, there may have been more than one, but the key one was when I tested the amp speaker binding post by replacing it with a different binding post that also had a steel tab.

Later when I tested the Purifi EVAL1 board (with built-in banana jacks) alongside the Buckeye board, the Purifi passed the test. At that point, was pretty convinced the culprit was the input board. I then tried several ways to alter the board grounding, but none worked. 

So, the troubleshooting effort turned towards the board designer as he had more intimate knowledge of the design. Lesson learned!