The ants need to have distended or full stomachs to kill them to get anything from them. Let them eat resources around the area before killing em. Giggi...dunno about that one, It always let me carve em.
Not sure about the Giggi, I've never seen them disappear before I could carve them.
For the Altaroths, try taking some Poison Smoke Bombs - throw one down in the middle of a group, wait for the poison to kill them, then carve their intact corpses. You should end up with Monster Fluid or Stomachs most of the time, with the occasional Jaw.
Granted, you don't need many stomachs for the Loc Lac gear, but you can save the rest for Bhanabra armor or sell them along with some of the Monster Fluids for a nice profit. --- XBL : Crossbit