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If I transfer things over for an in-game run, I prefer to make them feel more like in-game events rather than just exchanging a caught mon for another pokemon.
e.g, ORAS I wanted to use Clamperl/one of its evos since it was one of the few I never used in a run, but the issue was you got it so late so I bred a random one up, didn't trade it over until I got a rod from dewford and the moment I fished/caught a pokemon and caught it, I traded it over and imagined that I just fished up said Clamperl instead of a Tentacool.
Another example was when I played Alpha Sapphire and when I entered a patch of grass from the dexnav and kept finding Seviper, I imagined that one of them eventually was actually a Zangoose and they were just rare since it was a Seviper infested area since the whole rivalry. I caught said seviper, traded over a wild Zangoose and acted like nothing out the ordinary happened. Easily the most autistic so far.