The corthosis is a grade 6 mat, and thus only has a single moderate mission. On the plus side, IIRC there ARE only 5 total grade 6 missions, so this mission is always available, assuming it isn't already being run.
Thermoplast flux is a grade 5 mat, and thus has better missions (think both rich and bountiful), however there are far more than 5 grade 5 missions, so there is a distinct possibility none of the thermoplast missions will be available. (I don't *think* it has a grade 6 mission?)
Basically, if you're making augment kits, it's better/faster/cheaper to have your armstech/armormech make them than your synthweaver. (assuming, of course, you have multiple crewskills... which I do.
It's been a while since I really paid attention, but from what I remember, archeology is the only gathering skill that actually has a grade 6 "white" mat. The others cap out at grade 5.