Hrrrrm. Interesting; I don't think Corpse Constructs actually requires corpses, despite the name and the units essentially being beefed-up soulless. IIRC, I've done mass summonings of them (via the unique book, and perhaps also the lighting rod) in a capital province w/o corpses and still gotten 'em. Perhaps the caster was murdering the population to get them, but I didn't notice.
Haven't played Agartha for a long time, so I don't have any recollection of trying with flame corpses.
Aside from skills, another significant difference between them and the longdead is that longdead are poor amphibious, while soulless are landlubbers.