I've got a resolution this morning. CHECK THIS OUT!
I went outside to look at my season-old tires. I found weathered and cracked FIRESTONE tires in their place... ALL LT tow rating designation. Someone at chatfield swapped me tires when I was parked at the marina. What a scumbag person that must have been. Both rims were black, so I didn't notice it, but these have more grease on them.
I've replaced them with ShipShape Master tows rated at "D", and guess what? POOF! The sway is gone!