Rotating animated objects without messing up the animation

Sorry if this is basic knowledge, but I’m perplexed as to why I can’t rotate a set of objects that have been animated and retain the animation without messing it up. My intent is to eventually link or append this to another model/blend file.
Screen capture of what I’m running into:

The blend file:

Any help would be greatly appreciated.

Parent them to an empty and rotate the empty

select the object -> shift select the empty -> Ctrl P

Thanks, I’ll give that a try again, although I have an empty at the center but it isn’t listed in relations->parent type (probably overlooking something obvious).
FWIW - I also discovered just now that if I uncheck “z” under rotation in the dope sheet that it solves the issue.

Figured out how to parent the iris leaves to the empty and as I presumed, it was obvious.