Dear Eric,
" but I wanted to eliminate the easier answer before I start looking for the harder one."
ahh okay 
" The bug actually traces back to before 4.1.0 though it does seem to have gotten much worse in 4.2."
Oooh glad I helped you find it!
#Scaling IS the Bug!
" Do you do any sort of scaling to the character model and does that make the error worse, better, no different?"
Dear Eric,
When I use a static mesh actor that I drag into the world, using the simple material posted in this thread
with a Tessellation factor of 20 (yes I know that’s huge!!!
#Without Scaling
There is absolutely no distortion!
#You found the source of the bug!
Yaaaay!
#