Iirc, whatever we can stash in the character's personal rooms should be safe for the next loop. Aizawa already has a corner of his room dedicated to storing what equipment he can gather.

Ultimately, Aizawa doesn't care about Dax's theories, as long as they have similar plans and goals. The bigger picture isn't his focus-- he's focused on the practical details that can help the brainy types like Pal and Cecelia.

Not that he isn't smart. Someone just needs to keep things somewhat organized.

(Also, with luck, they might be able to open a channel to talk to Pal's ghost friends)