yeah, as it turns out, when it comes to constructing things, I am the intellectual inferior to Sean Penn in I am Sam.
Upon further review, I discovered that each of the arm chairs is branded with an L & and an R. L, for those like me who didn't know, represents "left" and "r" is for "right." I had them backward.
I remember thinking when I was putting them on (the first time) and noticed that they were scrunching up against the seat upholstry, "well, that's sure poor design engineering." I have a feeling that's what the engineers would say about me if they were a fly on the wall watching me being bested by an allen bolt.
I'm just pleased I managed to keep from putting them on upside down.
Well, twenty minutes and a second effort later, things are fixed and proper, and I have room to sit comfortably like a slacker whilst on the 'Net.