Day four update:
Still working well so far. Software is still terrible but it does work. The free LaserDRW seems to be better than the commercial CorelLASER (tied to CorelDRAW in a suspicious free trial deal) by virtue of its simplicity meaning a much more reliable piece of software.
LaserDRW only imports .emf vector files, all others are raster images. It also only allows for one task per file so you have to separate out your engraving from your cutting. Still completely usable, though.
CorelLASER does claim support for multiple tasks per job but a) the software crashes whenever we try to use it and b) since the cutter has no PWM drive from the controller you practically can't use it anyway.
We're currently investigating a controller swap since that would open up other software possibilities which may make things easier and more portable.