Alright I've seen you could use some help with your Giratina problem and I have some suggestions.
1) Evolve your Gastly, it will be stronger and capable of doing more. (So unless you really don't want to do so, I would evolve it.
... Shiny Mega Gengar is awesome.
) Another option would be to lvl up your Gastly to insane lvls like 80 and up.
2) I don't know if you thought of this and if it's still possible but Roselia learns GrassWhistle at lvl 22. SO I don't know if you thought your Roselia that move because then you might have a better chance at keeping it asleep.
3) You could learn your Staraptor Endure and Endeavor to get Giratina to 1 HP (Since none of your Shinies can learn False Swipe.)
4) Well there are more options but since you only want to use your BQ shinies you limit yourself pretty much to anything you already came up with yourself. (and my suggestions)
Anyways it's up to you which strategy you choose and ofcourse I wish you the best of luck with whatever strategy or hunt you will choose.