I have even more ideas!
When Regigigas arrives on the ship or maybe after she gives birth she could have a lot of stored information about ancient advanced technology that with the other three Regi's to construct a holo deck to perform "more efficient data collection". This could allow the legendries to have roleplay parts. Lugia in sexy teacher outfit and can say "You have been a bad student and need to be punished, you will do as I say". Raikou can be in sexy exercise outfit. Articuno feels like a sexy librarian outfit would fit on her and could say "Your book is overdue, pay the fee anyway you can". Suicune in distressed royalty outfit. A leopard bikini for one of the Pokémon. They can do a striptease with the holo cloths. The holo deck could simulate different environments like zero gravity, floating in the air, underwater without drowning, and more since it is very flexible to the imagination.
When Palkia joins she can modify the interior of the ship to be bigger since she controls space and would comment on it being to cramped for her liking but need "compensation" to do more.
An idea with the human relationship would be with Officer Jenny and her Growlthe and Nurse Jenny and her Chansy to help start the next generation of nurses and police. The MC reputation would have already become known to them and not turn away their Pokémon have childern as well as long as he has the right legendary as usual.
The MC could give a massage to his Pokémon.
A question is how far do you plan to take the incest? Will it be just brother and sister or could it go to mother and daughter or Father and daughter?