Had an idea for a few of the paradox Pokémon. For Iron Moth it is theorized to be an alien so she would abduct the MC and at light speed get him to another planet. She would be wearing an exo suite for travel in space and got the MC by teleportation to start the royal bloodline again for a space empire to be built descended from him. So after the sex Palkia shows up wondering why dinner has not been made yet since she would know where everything is at present and takes the MC back.
I could see the MC accidentally being sent back in time and meet one of the prehistoric paradox pokemon and Dialga brings him back to the present.
Giratina could be part of either Roaring Moon or Iron Jugulis scene somehow.
I can definitely see that Dialga would not like the Paldea region with the time travel, paradoxes that she once tried to fix but never could keep up with it so she just made sure it does not spread and would want to leave quickly since who knows when the next explosion of paperwork she would need to do comes. If Arceus has joined then Dialga would see this region as the most time she wasted in her life to fix something that just cant be fixed. Once she knows that the altering time is caused inadvertently by Terapagos she releases her frustration or anger on Terapagos but can decide to move on since the anomalies can now end in the region and will be keeping an eye on Terapagos.
Terapagos could be a reason the MC is able to taste the Milk of any Ultra Beasts he meet.