FINALLY. We figured it out.

For the past month or more, we have been going crazy trying to figure out why the dog had hives.
After trying everything possible to 'narrow it down,' the other morning it became surprisingly clear.
Lee has been on a kick lately with getting the yard in order, and with that he was kind enough to 'organize' my recycling bins out back for me.
He did this for 2 reasons,
ONE: to make it easier for me, and TWO: to keep Bentlee from dragging it out, chewing it up, and strewing it all over the back yard.
After doing so, Bentlee went an entire 36 hours without breaking out.
The next morning when we woke up, he was covered. AGAIN.
About an hour later, I went out back to throw a can in the bin, and discovered he had dumped one over, chewed, and INGESTED half of a milk carton, and a TON of cardboard.
After that, a dog beating followed, and a realization:
He was allergic to that crap.
Why it took us so long to figure it out? Who knows.
But the good news? We no longer have to keep him on steroids, and we no longer have a dog that embarasses us when we walk him down the street.