And, done! So you can indeed remove the shroud and get to the heatsink without having to remove the whole cooler. Have to undo the tiny Torx screws along the sides and top, then pry the shroud off and unscrew the big 4 philips head screws on the bottom to release the heatsink. NewerTech's kit didn't have a small enough Torx but I had a multitool that had the correct size.
I'd give the factory guys a C- on their thermal compound application. Not good, but not as horrible as some I've seen before (look for Macbook Pro thermal compound pictures if you want to see a real abomination). Cleaned off that stuff and replaced with Arctic MX-4.
No difference in full load temps, still tops out around 82-85˚C but I think that's GPU Boost doing its thing. No shut off issues even after putting it through the Furmark gauntlet (was kind of worried the lower temps would make it get more ambitious on the TDP, but it wasn't so).
HUGE difference in idle-midrange temps... Idle got as low as 33˚C (was idling around 45˚C previously). So yeah, big success here.