Shiny hunting conveniences

I don’t know of any way to re-encounter static encounter Pokémon, I think it would be cool/nice if you could release static encounter Pokémon and reset their encounter, for example the story encounter with Mew. I wish I could release my Mew and re fight him in the encounter to shiny hunt it instead of having to make a whole new game and play the whole story if I wanted to. Same goes for delta Pokémon like Raltz. Also I am new to shiny hunting in this game in general so if somebody could let me know what pokemon are shiny locked that would be nice