I'm guessing I found a bug then, because in the survival mission (that I did last) I brought Trin/Penta/Tombfinger/Vaykor Sydon, and I had all my mods. I didn't for the excavation or defense missions however. Is there some trick to mod layout that let's you bring them, maybe? I had Trin/Lenz/Prisma Angstrum/Ohma for the first two and didn't have my mods equipped. Interestingly, it seems that augments must work fine, or at least Octavia's "Conductor" augment.
As far as the mission itself, I find it a very interesting change of pace to the game to try and work without mods. I don't think a new frame's mission is something that should be easily cheese'd through like most missions, a challenge makes it that much more satisfying when you finish. It's not like you lose anything but time if you don't win, and in a game that's typically "press 4 to win" it makes an exciting change.