Late, but here I go:
Captain:
Iron Manta's seem a bit weird, and too weak effect for the high cost. I'm not sure when I would use this. Green Night is also a bit on the weak side, but it is much better thematically, and also a bit more useful. GFY is like a sundial that can be used every other turn, seems pretty OP, not really a fan. I don't really understand Paratus. The text implies the slot itseld gets destroyed, but the notes only seem to mean that it deals damage to something on the slot, not that the slot is destroyed. Random destruction is a bit weak since it can miss, but the theme is nice at least. (I gave GN most votes here)
Mapper:
I don't like Iron Manta's at all. (Espithel's was better, but I'm not basing my vote on that). The other 3 are pretty equal imo, and I (think) gave most votes to GFY and Paratus.
Space Trooper:
Iron Manta is my favorite here. The way the deck basically created a black hole (singularity) and then uses it offensively is cool. Paratus was a bit boring with only one element, GFY felt a bit all over the place with no single strategy, and GN was my second fav.
Log Keeper:
None were exactly what I had in mind, but IM had the most time dilation stuff, even if some artistic creativity was taken with "realism" (but I don't expect you all to be scientifically correct either, so don't worry)
Mechanic:
GFY and GN was the only submissions with an actual time travel mechanic, so they get my votes. I understand the thematic flavor of the other two submissions, but I would still want its effect to be more related to time travel.