andy,
It actually looks like the poly is still transparent, but
a) In your exported PDF (I assume at higher DPI than display) you're getting a different LOD of the hillshade in the basemap, which doesn't actually include the hillshade. Topo and other basemaps do this content change and higher LODs which trips us up all the time :/.
b) Your layout may be set to be CMYK, which means the colors would appear darker/muddier due to different gamut. you can check this in Layout properties dialog.
Jeremy W.