I got it working! (at least mostly)
I browserify'd MemoryDump.dat and spliced it into a local copy of the Gateway Go index.html; loading the page on my 3DS yielded a crashed browser and a 3MB memory.bin file on the SD card--perfect! Exactly as expected!
However, doing the same with LoadCode.dat as the JS string and code.bin copied to the SD card resulted in a very short flash of static on the lower screen and (probably 30 seconds) later, a browser crash--code execution regardless, but perhaps not as expected?
Actually, looking at code.c, I would expect it to only draw static once. But the static is immediately overwritten by the browser's framebuffer. I can even "use" the browser after exploit has executed. I can open "Menu" and Bookmarks and so on; the browser still crashes after 30 seconds, though. The screen becomes static for a frame and the browser crashes after 30 seconds, so the code is definitely executing, right? This is all very interesting!
And thank you, Yifan Lu, et al. I wouldn't call myself a 3DS developer or researcher, but as a person-what-sometimes-plays-with-devkitpro, I appreciate the immense amount of work that has gone into the scene.