Thanks guys. From reading around (albeit older posts) I think maybe the scale of these layers hits a memory limit when using the Dissolve function.
I have a layer of man-made cover for Canada that was WAY to unwieldy, so I broke it into provinces (which is how we want to handle the next part of analysis anyway), but I think there's still too many features. I think they're all single-part features to start with, I'm actually trying to make one multipart, but I think it might be too ambitious.
I've attached a windows snip of the British Columbia layer, with one of the output features selected. This layer started with 496924 features, and looks to have basically just dissolved 2 blocks. With denser provinces, the output breakdown is 4+ tiles like this.