The good news is that I was able to find an on-line copy of what appears to be volume II of Rabbi Posen, zt”l’s “Tavnis Ohalos” and print it for a small fee. I assume it’s volume II since it begins with chapter 3.
The site is Otzar Hahochma. I paid $6 (US) for a one-day pass and another $6 for printing rights.
As long as I had paid for access, I also printed out the author’s work “Tavnis Keilim”.
While I would prefer to have obtained both volumes and still hope to do so, I’m ecstatic to have just this. It’s exactly what I needed.
Thanks again to Sam2 for the reference.