Dave, thanks. I decided to keep this separate and hold off any questions on the push press, since that is a different animal.
I think that I did have close to the lower spine / hip position you mentioned, which seemed to exacerbate the pressure on the lower back and was thus my primary reason for concern. (Incidentally, the dip phase of the PP made this even worse, but I'll wait on that discussion).
So, should I expect that reduction in the severity of this lingering stress is something that will lesson with time and my press strengthens? My main hope as that this tightness is not an area of concern, but it's several hours later now and I don't notice any lingering nagging pain in my lower back. If these are normal stressors on the musculature and "part of the deal," so to speak, then I'll just carry on.