Oops, forgot to mention that earlier - the .shp files are coming out at around 320mb and the .dbf's are around 50mb. Likewise the rasters aren't very large; only about 10mb.
EDIT: For kicks I tried performing the task on another raster and it was successful, so there's something about this particular group of rasters that's causing the issue. I'm going to clip out a small chunk of one of them to get the file size down and upload it here, maybe that will help.